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s\- ^^^ REPORT OF THE FIFTY-FIFTH MEETING OP THE BRITISH ASSOCIATION FOR THE ADVMCEMENT OF SCIENCE; HELD AT ABERDEEN IN SEPTEMBER 1885. LONDON : JOHN MURRAY, ALBEMARLE STREET. 1886. Office of tne Association : 22 Albemarle Steeet, London, W. PRINTED BY 8P0TTI8W00DE AND CO., NEW-STEBET SQUARE LONDO.V CONTENTS. Page Objects and Rules of the Association xxyii Places and Times of Meeting and Officers from commencement xxxy i Presidents and Secretaries of the Sections of the Association from com- mencement xUii Evening Lectures Ivii Lectures to the Operative Classes Ix Officers of Sectional Committees present at the Aberdeen Meeting Ixi Treasurer's Account Ixiii Table showing the Attendance and Receipts at the Annual Meetings Ixiv Officers and Council, 1885-86 Ixvi Report of the Council to the General Committee livii Tlecommendations adopted by the General Committee for Additional Reports and Researches in Science Ixxi Synopsis of Grants of Money Ixxix Places of Meeting in 1886 and 1887 Ixxx jeneral Statement of Sums which have been paid on account of Grants for Scientific Purposes Ixxxi rrangement of theGeneral Meetings xcii i-ddress by the President, the Right Hon. Sir Lyon Platfaie, K.C.B., M.P., F.R.S 1 * EEPORTS ON THE STATE OF SCIENCE. Report of the Committee, consisting of Professor G. Carey Foster, Sir W. Thomson, Professor Ayrton, Professor J. Perry, Professor W. G. Adaks, Lord Rayleigh, Dr. 0. J. LpDGE, Dr. John Hopkinson, Dr. A. Mtjirheab, Mr. W. H. Preece, Mr. H. Taylor, Professor Everett, Professor Schus- ter, Dr. J. A. Fleming, Professor G. F. Fitzgerald, Mr. R. T. Glaze- brook (Secretary), Professor Chrystal, Mr. H. Tomlinson, and Professor W. Garnett, appointed for the purpose of constructing and issuing practical Standards for use in Electrical Jleasurements 31 Report of the Committee, consisting of Professors A. Johnson (Secretary), J. G. MacGregoh, J. B. Cherriman, and H. T. Botey and Mr. C. Carpmael, appointed for the purpose of promoting Tidal Observations in Canada 8u A3 IV CONTENTS. Page Fifth Report of the Committee, consisting of Mr. John Murkat (Secretary), Professor Schttster, Professor Sir William Thomson, Professor Sir H. E. RoscoE, Professor A. S. IIerschel, Captain W. de W. Abnet, Professor Bonnet, Mr. R. H. Scott, and Dr. J. H. Gladstone, appointed for the pur- pose of investigating the practicability of collecting and identifying Meteoric Dust, and of considering the question of undertaking regular observations in various localities 34 Third Report of the Committee, consisting of Professors G. H. Darwin and J. C. Adams, for the Harmonic Analysis of Tidal Observations. Drawn up by Professor G. H. Darwin 35 Report of the Committee, consisting of Mr. Robert H. Scott (Secretary), Mr. J. Norman Lockter, Professor G. G. Stokes, Professor Balfour Stewart, and Mr. G. J. Stmons, appointed for the purpose of co-operating with the Meteorological Society of the Mauritius in their proposed publica- tion of Daily Synoptic Charts of the Indian Ocean from the year 1861. Drawn up by Mr. R. H. Scott 60 Rejjort of the Committee, consisting of Mr. James N. Shoolbred (Secre- tary) and Sir William Thomson, appointed for the reduction and tabulation of Tidal Observations in the English Channel, made with the Dover Tide-gauge ; and for connecting them with Observations made on the French coast 60 Report of the Committee, consisting of Professor G. Forbes (Secretary), Captaiu Abnet, Dr. J. IIopkinson, Professor W. G. Adams, Professor G. C. Foster, Lord Ratleigh, Mr. Preece, Professor Schuster, Professor Dewar, Mr. A. Veknon Harcourt, and Professor Atrton, appointed for the purpose of reporting on Standards of "V\'hite Light. Drawn up by Professor G. Forbes 61 Second Report of the Committee, consisting of Professor Balfour Stewart (Secretary), Mr. J. Knox Laughton, Mr. G. J. Symons, Mr. R. H. Scott, and Mr. Johnstone Stoney, appointed for the purpose of co-operating with Mr. E. J. Lowe in his project of establishing a Meteorological Observatory near Chepstow on a permanent and scientific basis 64 Report of the Committee, consisting of Professor Balfour Stewart (Secretary), Sir W. Thomson, Sir J. H. Lefroy, Sir Frederick Evans, Professor G. H. Darwin, Professor G. Chrystal, Professor S. J. Perry, Mr. C. H. Caepmael, and Professor Schuster, appointed for the purpose of considering the best means of Comparing and Reducing Magnetic Observa- tions. Drawn up by Professor Balfour Stewart 65 Report of the Committee, consisting of Professor Crum Brown (Secretary), Mr. MiLNE-HoME, Mr. John Murray, and Mr, Buchan, appointed for the purpose of co-operating with the Scottish Meteorological Society in making Meteorological Observations on Ben Nevis 90 Seventeenth Report of the Committee, consisting of Professor Everett, Pro- fessor Sir AV. Thomson, Mr. G. J. Symons, Sir A. C. Ramsay, Dr. A. Geikib, Mr. J. Glaisher, Mr. Pengellt, Professor Edward Hull, Professor Prestwich, Dr. C. Le Neve Foster, Professor A. S. Herschel, Professor G. A. Lebour, Mr. Galloway, Mr. Joseph Dickinson, Mr. G. F. Deacon, Mr. E. Wexhered, and Mr. A. Strahan, appointed for the purpose of investigating the Rate of Increase of Underground Temperature downwards in various Localities of Dry Land and under Water. Drawn up by Professor Everett (Secretarj-) 93 Report on Electrical Theories. By Professor J. J. Thomson, M.A., F.R.S — 97 Second Report of the Committee, consisting of Professor Schuster (Secretary), Professor Balfour Stewart, Professor Stokes, Mr. G. Johnstone Sxoney, Professor Sir H. E. RoscoE, Captain Abney, and Mr. G. J. Symons, ap- pointed for the purpose of considering the best methods of recording the direct Intensity of Solar Radiation 56 CONTENTS. V Page Report on Optical Theories. By R. T. Glazebrook, M.A., F.R.S 157 Report of the Committee, consisting of Professors Ramsay, Tilden, Mar- shall, and W. L. Goodwin (Secretary), appointed for the purpose of investigating certain Physical Constants of Solution, especially the Expan- sion of Saline Solutions 261 Third Report of tlie Committee, consisting of Professors Williamson, Dewar, Feankland, Crum Brown, Obling, and Armstrong, Drs. Hugo Muller, r. R. Japp, and H. Forster Morlex, and Messrs. A. G. Vernon Har- coFRT, C. E. Groves, J. Millar Thomson, H. B. Dixon (Secretary), and V. H. Velet, reappointed for the purpose of drawing up a statement of the varieties of Chemical Names which have come into use, for indicating the causes which have led to their adoption, and for considering what can be done to bring about some convergence of the views on Chemical Nomen- clature obtaining among English and foreign chemists 262 Report of the Committee, consisting of Professors Odling, Huntington, and Hartley, appointed to investigate by means of Photography the Ultra- violet Spark Spectra emitted by Metallic Elements and their combinations under varying conditions. Drawn up by Professor W. N. Hartley, F.R.S. (Secretary) 276 Report of the Committee, consisting of Professor Tilden, Professor W. Ramsay, and Dr. W. W. J. Nicol (Secretary), appointed for the purpose of investigating the subject of Vapour Pressures and Refractive Indices of Salt Solutions 284 Report of the Committee, consisting of Professor Sir H. E. Roscoe, Mr. J. N. Lockyer, Professors Dewar, Wolcott Gibbs, Liveing, Schuster, and W. N. Hartley, Captain Abney, and Dr. Marshall Watts (Secretary), appointed for the purpose of preparing a new series of AVave-length Tables of the Spectra of the Elements and Compounds 288 Thirteenth Report of the Committee, consisting of Professors J. Prestwich, W. Boyd Dawkins, T. McK. Hughes, and T. G. Bonney, Dr. H. W. Geosskey (Secretary), Dr. Deane, and Messrs. C. E. De Range, H. G. FoRDHAM, J. E. Lee, D. Mackintosh, W. Pengelly, J. Plant, and R. H. TiDDEMAN, appointed for the purpose of recording the position, height above the sea, lithological characters, size, and origin of the Erratic Blocks of England, Wales, and Ireland, reporting other matters of interest con- nected with the same, and taking measures for their preservation 322 Third Report of the Committee, consisting of Mr. R. Etheridge, Dr. H. WooDAVARD, and Professor T. Rupert Jones (Secretary), on the Fossil Phyllopoda of the Palaeozoic Rocks 326 Fifth Report of the Committee, consisting of Mr. R. Etheridge, Mr. Thomas Gray, and Professor John Milne (Secretary), appointed for the purpose of investigating the Earthquake Phenomena of Japan. Drawn up by the Secretary 362 Eleventh Report of the Committee, consisting of Professor E. Hull, Dr. H. W. Ceosskey, Captain Douglas Galton, Professors J. Pkesiwich and G. A. Lebour, and Messrs. James Glaisher, E. B. Marten, G. H. Morton, James Parker, W. Pengelly, James Plant, I. Roberts, Fox Steangways, T. S. Stooke, G. J. Symons, W. Toplet, Tylden-Wright, E. Wethered, W. Whitaker, and C. E. De Range (Secretary), ap- pointed for the purpose of investigating the Circulation of Underground Waters in the Permeable Formations of England and Wales, and the Quantity and Character of the Water supplied to various Towns and Dis- tricts from these Formations. Drawn up by C. E. De Range 380 VI CONTENTS. Page- Eeport of the Committee, consisting of Mr. H. Batterman, Mr. F. AV. Rtjdler, and Dr. H. J. Johnston-Lavis, for the Investigation of the Volcanic Plieuomena of Vesuvius. Drawn up by H. J. Johnston-Lavis, M.D., F.G.S. (Secretary) 395 Report of the Committee, consisting of i\L'. W. T. Blanfoed and Mr. J. S. Gaedxer (Secretary), on the Fossil Plants of the Tertiary and Secondary Beds of the United" Kingdom. Drawn up by Mr. J. S. Gaednee, F.G.S", F.L.S 396- Report of the Committee, consisting of Messrs. R. B. Grantham, C. E. De Rance, J. B. Redman, W. Toplet, W. Whitakee, and J. W. Woodall, Major-General Sir A. Claeke, Sir J. N. Douglass, Captain Sir F. 0. Evans, Admiral Sir E. Ommanney, Captain J. Parsons, Professor J. Peestavicu, Captain W. J. L. Whaeton, and Messrs. E. Easton, J. S. Valentine, and L. F. Vernon Haecottrt, appointed for the purpose of inquiring into the Rate of Erosion of the Sea-coasts of England and Wales, and the Influence of the Artificial Abstraction of Shingle or other Material in that Action. 0. E. De Rance and "W. Topley, Secretaries ; the Report edited by W. Toplet 404 Report of the Committee, consisting of Professor Rat Lankester, Mr. P. L. Sclater, Professor M. Foster, Mr. A. Sedgavick, Professor A. M. Mar- shall, Professor A. C. Haddon, Professor Moselet, and Mr. Peect- Sladen (Secretary), appointed for the purpose of arranging for the occu- pation of a Table at the Zoological Station at Naples 466' Report of the Committee, consisting of Professor McIvendeick, Professor Struthers, Professor Young, Professor McIntosh, Professor Alletne Nicholson, Professor Cossar Ewaet, and Mr. John Mxjrrat (Secretary), appointed for the purpose of promoting the establishment of a Marine Biological Station at Granton, Scotland 474 Report of the Committee, consisting of Sir Lton Platfair, Professor IVIose- I.ET, Admiral Sir E. Ommanney, Mr. P. L. Sclater, and Mr. A. Sedgwick (Secretary), appointed to prepare a Report on the Aid given by the Do- minion Government and the Government of the United States to the encouragement of Fisheries, and to the investigation of the various forms of Marine Life on the coasts and rivers of North America 479' Report of the Committee, consisting of Professor Huxlet, Mr. Sclater, Mr. Howard Saunders, Mr. Thiselton Dter, and Professor Moselet (Secretary), appointed for the purpose of promoting the establishment of Marine Biological Stations on the coast of the United Kingdom 480' Report of the Committee, consisting of Dr. H. C. Soebt and Mr. G. R. Vine, appointed for the purpose of reporting on recent Polyzoa. Drawn up by Mi: G. R. Vine 481 Third Report of the Committee, consisting of Sir J. Hooeee, Dr. Qunthbr, Mr. HowAED Saundees, and Mr. Sclatee (Secretary), appointed for the purpose of exploring Kilima-njaro and the adjoining mountains of Equa- torial Africa 681 Report of the Committee, consisting of Mr. John Coedeaux (Secretary), Professor A. Newton, Mr. J. A. Haevie-Beown, Mr. William Eagle Claeke, Mr. R. M. Barrington, and Mr. A. G. More, appointed for the purpose of obtaining (with the consent of Master and Brethren of the Trinity House and the Commissioners of Northern and Irish Lights) observations on the Migration of Birds at Lighthouses and Ligh tvessels, and of reporting on the same 685- CONTENTS. Vll Page Eeport of the Committee, consistiog of General Sir J. H. Lefrot, Lieut.- Colonel GoDWiN-AtrsTEN-, Mr. W. T. Blajiford, Mr. Sclater, Mr. Carrtjthers, Mr. Thiselton-Dter, Professor Struthers, Mr. G. W. Bloxam, Mr. H. W. Bates (Secretary), Lord Alfred Ghtirchill, ilr. F. Galton, and Professor Moselet, appointed for the pui-pose of furthering the Exploration of New Guinea by making a grant to Mr. Forbes for the purposes of his expedition 690 Report of the Committee, consisting of General Sir J. H. Lefrot, the Rev. Canon Carver, Mr. F. Galton, Mr. P. L. Sclater, Professor Moselet, Dr. E. B. Tilor, Professor Boyd Dawkins, Mr. G. W. Bloxam, and Mr. H. W. Bates (Secretary), appointed for the purpose of furthering the scientific examination of the country in the vicinity of Mount Roraima in Guiana, by making a grant to Mr. Everard F. im Thurn for the purposes of his expedition 6y0 Report of the Committee, consisting of the Rev. Canon Tristram, the Rev. F. Lawrence, and Mr. James Glaisher (Secretary), appointed for the purpose of promoting the Sur\ey of Palestine 691 Report of the Committee, consisting of Dr. J. H. Gladstone (Secretary), Mr. William Shaen, Mr. Stephen Bourne, Miss Ltdia Becker, Sir John Lubbock, Dr. H. "W. Crossket, Sir Richard Temple, Sir Henrt E. RoscoE, Mr. James Hetwood, and Professor N. Stoet Maskeltne, appointed for the purpose of continuing the inquiries relating to the teachbg of Science in Elementary Schools 692 Report of the Committee, consisting of Sir Frederick Bramwell (Secre- tary), Professor A. "W. Williamson, Professor Sir William Thomson, Mr. St. John Vincent Dat, Sir F. Abel, Captain Douglas Galton, Mi-. E. H. Carbutt, Mr. Macrort, Mr. H. Trueman Wood, Mr. W. H. Barlow, Mr. A. T. Atchison, Sir R. E. Webster, Mr. A. Carpmael, Sir John Lubbock, Mr. Theodore Aston, and Mr. James Brunlees, appointed for the purpose of watcliing and reporting to the Council on Patent Legislation 695 Report of 4he Committee, consisting of Dr. E. B. Ttloe, Dr. G. M. Dawson, General Sir J. H. Lefrot, Dr. Daniel Wilson, Mr. Horatio Hale, Mr. R. G. Haliburton, and Mr. Georgse W. Bloxam (Secretary), appointed for the pm-pose of investigating and publishing reports on the physical characters, languages, and industrial and social condition of the North-western Tribes of the Dominion of Canada Report to the Council of the Corresponding Societies Conxmittee, consistin"' of Mr. Francis Galton (Chairman), Professor A. W. Williamson^ Captain Douglas Galton, Professor Botd Dawkins, Sir Rawson Rawson, Dr. Gakson, Dr. J. Evans, Mr. J. Hopkinson, Professor Meldola (Secretary), Mr. W^hitaker, Mr. G. J. Stmons, and Mr. H. George Fobdham 708 On Electrolysis. By Professor Oliver J. Lodge, D.Sc 723 A Tabular Statement of the Dates at which, and the Localities where, Pumice or Volcanic Dust was seen in the Lidian Ocean in 1883-84. By Charles Meldeum, F.R.S 773 List of Works on the Geology, Mineralogy, and Palseontology of Stafford- shire, Worcestershire, and Warvriickshire. By William Whitaker, B.A., F.G.S., Assoc.Inst.C.E 780 On Slaty Cleavage and allied Rock-Structures, with special reference to the Mechanical Theories of theii- Origin. By Alfred Harkeb, M.A., F.G.S. ^^'^ VUl CONTENTS. Page On the Strength of Telegraph Poles. By W. H. Preece, F.E.S., M.Inst.O.E 853 On the Use of Index Numbers in the Investigation of Trade Statistics. By Stephen Bourne, F.S.S 859 The Forth Bridge Works. By Andrew S. Biggart, C.E 873 Electric Lighting at the Forth Bridge Works. By James N. Shoolbred, B.A., M.Inst.O.E 879 The New Tay Viaduct. By Crawford Barlow, B.A., M.InstO.E 883 TEANSACTIONS OF THE SECTIONS. Section A.— MATHEMATICAL AND PHYSICAL SCIENCE. THURSDAY, SEPTEMBER 10. Page Address bj- Professor G. Chrtstal, M.A., F.R.S.E., President of the Section 889 1. On the Dilatancy of Media composed of Eigid Particles in Contact. By Professor Osborne Reynolds, M.A., F.R.S 896 2. On Calculating the Surface Tension of Liquids by means of Cylindrical Drops or Bubbles. By Professor G. PiRiE, M.A 898 3. On the Suiface Tension of Water which contains a Gas dissolved ia it. By Professor G. Pieie, M.A 898 4. Thermod-\-namic Efficiency of Thermopiles. By Lord Ratleigf, D.C.L., LL.D., F.R.S 898 6. On the Measm-ement of the Intensity of the Horizontal Component of the Earth's Magnetic Field. By Thomas Gray, B.Sc, F.R.S.E 898 6. On Atmospheric Electricity. By Professor C. Michie Smith, B.Sc, F.R.S.E 899 7. Molecular Distances in Galvanic Polarisation. By Professor J. Larmor, M.A 900 8. On the Employment of Mance's Method for eliminating the Effects of Polarisation, to determine the Resistance of the Human Body. Bv Dr. W. H. SxoNE, M.A .' 900 9. On Contact Electricity in Common Air, Vacuum, and different Gases. By J. T. BoTTOMLEY, M.A., F.R.S.E 901 10. On a Specimen of almost Unmagnetisable Steel. By J. T. Bottomlet, M.A., F.R.S.E 903 11. On the Cooling of Wires in Air and in Vacuum. By J. T. Bottomlet, M.A., F.R.S.E 904 FBIDAY, SEPTEMBER 11. 1. On Kinetic Theories of Matter. By Professor A. CRinu: Brown, M.D., F.R.S 904 2. On Kinetic Theories. By Professor G. D. Liveing, M.A., F.R.S 904 3. On Thermal Effusion and the Limiting Pressure in Polarised Gas. By G. JoHNSTONi! Stoney, LL.D., F.R.S 904 4. On a Law concerning Radiation. By Professor Schuster, Ph.D., F.R.S. 905 5. On Boltzmaun's Theorem. By Professor W. M. Hicks, M.A., F.R.S. ... 905 X co:ntEiNts. Page 6. The Rate of Explosion of Hydrogen and Oxygen. By H. B. Dixon, M.A. 905 7. Report of the Committee for constructing and issuing practical Standards for use in Electrical Measurements 905 8. Report on Electrical Theories. By Professor J. J. Thomson, M.A., F.R.S. 905 9. On Constant Gravitational Instruments for measuring Electric Currents and Potentials. By Professor Sir W. Thomson, LL.D., F.R.S 905 10. On a method of multiplying Potential from a hundred to several thousand Volts. By Professor Sir William ThomsOxV, LL.D., F.R.S 907 11. On a form of Mercury Contact Commutator of Constant Resistance for use in adjusting Resistance Coils by Wheatstone's Bridge, and for other purposes. By Professor J. Viriamu Jones 907 12. On Slide Resistance Coils -with ftlercury Contacts. By Professor J. ViBiAMTT Jones 907 13. On the relative Merits of Iron and Copper Wire for Telegraph Lines. By W. H. Peeece, F.R.S 907 SATURDAY, SEPTEMBER 12. 1. On Orthoptic Loci. By the Rev. C. Taylor, D.D 909 2. On the Reduction of Algebraical Determinants. By "\V. H. L. Russell, F.R.S 910 3. Account of the Levelling Operations of the Great Trigonometrical Survey of India. By Major A. W. Baikd, R.E., F.R.S 911 4. A Theorem relating to the Time-moduli of Dissipative Systems. By Lord Ratleigh, D.C.L., LL.D., F.R.S 911 5. On a new Polariser devised by Mr. AJirens. By Professor Silvanits P. Thompson, D.Sc 912 6. On a simple Modification of the Nicol Prism giving "Wider Angle of Field. By Professor Silvanus P. Thompson, D.Sc 912 7. On some of the Laws which regulate the Sequence of Mean Temperature and Rainfall in the Climate of London. By II. Coitrtenat Fox, M.R.C.S. 912 8. Notes upon the Rotational Period of the Earth and Revolution Period of the Moon deduced from the Nebular Hypothesis of Laplace. By W. F. Stanley, F.G.S., F.R.M.S 915 9. On a Galvanic Battery. By C. J. Burnett 916 MONDAY, SEPTEMBER U. 1. Report of the Committee on Standards of White Light 916 2. Photometry with the Pentane Standard. By A. Vernon Harcouet, M.A., F.R.S 916 3. On a Photometer made with Translucent Prisms. By J. Joly, B.E 917 4. Report of the Committee for reducing and tabulating the Tidal Obser- vations in the English Channel, made with the Dover Tide-gauge ; and for connecting them with Observations made on the French coast 917^ 5. Seventeenth Report of the Committee on Underground Temperature 917 6. Fifth Report of the Committee on Meteoric Dust 917 7. A Tabular Statement of the Dates at which, and the Localities where, Pumice or Volcanic Dust was seen in the Indian Ocean in 1883-84. By Charles Meldrum, F.R.S 917" CONTENTS. xi 8. Eeport of the Committee for co-operating with the Meteorological Society of the Mauritius in their proposed publication of Daily Synoptic Charts of the Indian Ocean from the year 1861 917 9. Daily Synoptic Charts of the Indian Ocean. By Charles Meldexjjt, F.E.S. 917 10. Eeport of the Committee appointed to co-operate with the Scottish Meteorological Society in making Meteorological Observations on Ben Nevis 917 11. On the Meteorology of Ben Xevis. By Alexander Buchan 917 12. On some Eesults of Observations with kitewire-suspended Anemometers up to 1,300 feet above ground, or 1,800 feet above sea-level, in 1883-85. By E. Douglas Archibald 9^9 13. On the Measurement of the Movements of the Ground, with reference to proposed Earthquake Observations on Ben Nevis. Bv Professor J \ EwiNG, B.Sc, F.E.S.E \' ' 920 14. On the supposed Change of Climate in the British Isles within recent years. By Thomas Heath,B.A 922 15. On Malvern, Queen of Inland Health Eesorts, and on improved Hygro- metric Observations. By Professor C. Piazzi Smyth, F.E.S.E 922 16. The Annual Eainfall of the British Islands. By Alexander Buchan ... 923 17. Eemarkable Occurrence during the Thunderstorm of August 6, 1885, at Albrighton. By J. Bedford Elwell ? .',.., 924 18. On a supposed Periodicity of the Cyclones of the Indian Ocean south of the Equator. By Charles Meldrum, F.E.S 926 19. A new Wind Vane or Anemoscope, specially designed for the use of Meteorologists. By G. M. Whipple, B.Sc, F.E.A.S 926 ■ 20. On the Third Magnetic Survey of Scotland. By Professor T. E. Thorpe F.E.S., and A. W. Eucker, F.E.S ' 926 TUESDAY, SEPTEMBER 15. 1. Eeport of the Cormnittee for considering the best means of Comparing and Eeducing Magnetic Observations 928 2. Eeport of the Committee for considering the best methods of recordino- the direct Intensity of Solar Eadiation ° 923 3. On a means of obtaining constant known Temperatures. By Professor W. Eamsat, Ph.D., and Sydney Young, D.Sc 928 4. On certain facts in Thermodynamics. By Professor W Eamsay Ph D and Sydney Young, D.Sc ' '928 5. Eeport on Optical Theories. By E. T. Glazebrooe:, M.A., F.E.S 929 6. On a Point in the Theory of Double Eefraction. By E. T. Glazebrook, M.A., F.E.S 929 7. Exhibition of a Mechanical Model illustrating some propert'es of the Ether. By G. F. Fitzgerald, F.E.S 93O 8. On the Constitution of the Luminiferous Ether on the Vortex Atom Theory. By Professor W. M. Hices, M.A., F.E.S 930 9. On an improved Apparatus for Christiansen's Experiment. Bv Lord Eayleigh, D.C.L., LL.D., F.E.S 930 10. Optical Comparison of Methods for observing small Eotations Bv Lord Eayleigh, D.C.L., LL.D., F.E.S 930 11. On the Accuracy of Focus necessary for sensibly perfect Definition Bv Lord Eayleigh, D.C.L., LL.D., F.E.S .'....... 930 XU CONTENTS Page 12. On Electro-Optic Action of a Charged Franklin's Plate. By J. Kerb, LL.D 930 13. On Magnetic Double Circular Refraction. By De Witt B. Brace, Ph.D. 931 14. Determination of the Heliographic Latitude and Longitude of Sun-spots. By Professor A. W. Thomson 931 WEDXESDAT, SEPTEMBER 16. 1. On the Nature of the Corona of the Sun. By William Huqgins, D.C.L., LL.D., F.R.S 932 2. On the Spectrum of the SteUa Nova visible on the Great Nebula in An- dromeda. By William HuGsiNs, D.C.L., LL.D., F.R.S 935 3. On the Bright Star iu the Great Nebula in Andromeda. By Ralph COPELAND, Ph.D 935 4. On Solar Spectroscopy in the Infra Red. By Dr. Daniel Draper 936 ^. The Errors of Sextants as indicated by the Records of the Verification Department of the Kew Observatory, Richmond, Surrey. By G. M. Whipple, B.Sc, F.R.A.S ". 936 6. On the Behaviour of First-class Watches whilst undergoing tests in the Rating Department of the Kew Observator}-, Richmond, Surrey. By G. M. Whipple, B.Sc, F.R.A.S 937 7. On a recent Improvement in the Construction of Instruments graduated upon Glass. By G. M. Whipple, B.Sc, F.R.A.S 937 8. On Methods of preventing Change of Zero of Thermometers by Age. By G. M. Whipple, B.Sc, F.R.A.S 938 9. On a new and simple form of Calorimeter. By Professor W. F. Barrett 938 10. On a modification of the Dauiell Battery, using Iron as Electropositive Element. By J. J. Coleman 938 11. On a new form of Galvanometer. By Professor James Bltth, M.A., F.R.S.E 939 12. On the Physical Conditions of Water in Estuaries. By Hugh Robert Mill, B.Sc, F.R.S.E., F.C.S 940 13. Further Experiments in Photo-Electricity. By Professor Minchin 940 14. On the Formation of a Pui-e Spectrum by Newton. By G. Griffith, M.A 940 16. On the Use of Bisulphide of Carbon Prisms for cases of Extreme Spectro- scopic Dispersion, by Professor C. Piazzi Smyth ; and their Results in Gaseous Spectra, commented on by Professor Alexander S. IIerschel, M.A., F.R.S 942 Section B.— CHEMICAL SCIENCE. THURSDAT, SEPTEMBER 10. Address by Professor H. E. Armstrong, Ph.D., F.R.S., Sec.C.S., President of the Section 946 1. Report of the Committee appointed for the purpose of investigating by means of Photography the Ultra- Violet Spark Spectra emitted by Metallic Elements and their combinations under varying conditions 965 2. On the Non-existence of Gaseous Nitrous Anhydride. By Professor William Ramsay, Ph.D., and J. Tudor Cundall 965 CONTENTS. Xlll Page 3. On some Actions of a Groves's Gas-battery. By Professor William Kamsat, Ph.D 965 4. On the Spontaneous Polymerisation of Volatile Hydrocarbons at tlie ordinary atmospheric temperature. By Professor Sir Henet E. Roscoe, F.R.S.1 967 5. On some new Vanadium Compounds. By J. T. Brieelet 968 FRIDAY, SEPTEMBER 11. 1. On the Essential Elements of Plants. By T. Jamieson 969 2. The Periodic Law, as illustrated by certain physical properties of Organic Compounds. By Professor Thos. Caenellt, D.Sc 969^ 3. Suggestions as to the Cause of the Periodic Law and the Nature of the Chemical Elements. By Professor Thos. Caenellt, D.Sc 969 4. On the Value of the Refraction Goniometer in Chemical work. By Dr. J. H. Gladstone, F.R.S 970 5. On the Refraction of Fluorine. By Geoege Glabstone, F.C.S 970 6. Note on some Conditions of the Development, and of the Activity, of Chlorophyll. By Profe.ssor J, H. Gilbebt, LL.D., F.R.S 970 7. A Plea for the Empiric Naming of Organic Compounds. By Professor Odling, F.R.S 972 8. On the Action of Sodium Alcoholates on Fumaric and Maleic Ethers. By Professor Pttrdie, Ph.D., B.Sc 972 9. On Sulphine Salts derived from Ethylene Sulphide. By Okste Masson, M.A., D.Sc 974 10. An apparently new Hydrocarbon distilled from Japanese Petroleimi. By Dr. DivEES and T. Nakamuea 975 11. Description of some new Crystallised Combinations of Copper, Zinc, and Iron Sulphates. By John Spillee, F.C.S 976 SATURDAY, SEPTEMBER 12. 1. The Composition of Water by Volume. By A. Scott, M.A., D.Sc F.R.S.E 976 2. Description of a new Mineral from Loch Bhruithaich, Inverness-shire. By W, IvisoN Macadam, F.C.S., and Thomas Wallace 977 3. Exhibition and Description of the apparatus employed in obtaining Oxygen and Nitrogen from the Atmosphere. Description of method used in converting Atmospheric Nitrogen into Ammonia. By Messrs. Bein Brothers 977 MONDAY, SEPTEMBER 14. 1. Report of the Committee on Chemical Nomenclature 977 2. On Electrolysis. By Professor Olivee J. Lodge, D.Sc 977 3. On Helmholtz's views on Electrolysis, and on the Electrolysis of Gases. By Professor Schustee, F.R.S 977 4. On the Determination of Chemical Affinity in terms of Electromotive Force. By 0. R. Aldee Weight, D.Sc, F.R.S 973. o. On the Sensitiveness to Light of Selenium and Sulphur Cells. By Shel- EOED BiDWELL, M.A., LL.B 98L Xiv CONTENTS. Page 6. On the Generation of a Voltaic Current by a Sulphur Cell with a Solid Electrolyte. By Shelford Bidwell, M.A., LL.B 982 7. A Theory of the Connection between the Crystal Form and the Atom Composition of Chemical Compounds. By William Baelow 983 S. On the use of Sodium or other soluble aluminates for softening and purify- ing bard and impure water and deodorising and precipitating sewage, waste water from factories, &c. By F. Maxwell Ltte, F.C.S 984 TUESDAY, SEPTEMBER 15. 1. Report on Vapour Pressures and Refractive Indices of Salt Solutions 985 2. Report on certain Physical Constants of Solution 985 3. On Solutions of Ozoue and the Chemical Actions of Liquid Oxygen. Bv Professor Dewak, F.R.S .". 985 4. On Physical Molecular Equivalents. By Professor Guthrie, F.R.S 985 5. The Size of Molecules. By Professor A. W. Reinold, M.A., F.R.S 986 6. An approximate determination of the Absolute. Amounts of the Weights of the Chemical Atoms. By G. Johnstone Stoxet, D.Sc, F.R.S 987 7. On Macromolecules (^lolecules of Matter in the CJrystalline State as dis- tinct from the Chemical Molecule), and determinations of some of them. By G. Johnstone Stonet, D.Sc, F.R.S 988 8. On the Dilatancy of Media composed of Rigid Particles in Contact. By Professor Osborne Reynolds, M.A., F.R.S 989 9. On the Evidence deducible from the Study of Salts. By Spencer U. Pickering 989 10 On the Molecular Weights of Solids and Salts in Solution. By Professor W. A. TiLDEN, D.Sc, F.R.S 990 11. On the Moleculai- Constitution of a Solution of Cobaltous Chloride. By Professor W. J. Rtissell, Ph.D., F.R.S 991 WEDNESDAY, SEPTEMBER 16. 1. An Electro-centrifugal ^Machine for Laboratory use. By Alexander Watt, F.I.C, F.C.S 991 2. Barium Sulphate as a Cementing Material in Sandstone. By Professor Frank Clowes, D.Sc 992 3 An Apparatus for determining the Viscosity of Oils. By A. H. Allen, F.C.S 992 4. The Action of Nitrous Gases upon Amyl Alcohol. Bv J. Williams, F.C.S., F.I.C, and Mtles H. Smith, F.C.S .". 992 6. On the Action of Water on Lead. By A. II. Allen, F.C.S 993 Section C— GEOLOGY. THURSDAY, SEPTEMBER 10. Address by Professor J. W. Jtjdd, F.R.S., Sec.G.S., President of the Section 994 1. Report on the Volcanic Phenomena of Vesuvius 1013 2. Fifth Report on the Earthquake Phenomena of Japan 1013 3. On some recent Earthquakes on the Durham Coast, and their probable cause. By Professor G. A. Lebotjr, M.A., F.G.S 1013 CONTENTS. IV Page 4. Notice of an Outline Geological Map of Lower Egj-pt, Arabia Petrsea, and Palestine. By Professor Edward Hull, LL.D., F.R.S., F.G.S. ... 1015 5. On the Occurrence of Lower Old Red Conglomerate in the Promontory of the Fanad, North Donegal. By Professor Edward Hull, LL.D., F.R.S., F.G.S 1016 6. On Bastite-Serpentine and Troktolite in Aberdeenshire ; with a Note on the Rock of the Black Dog. By Professor T. G. Bonnet, D.Sc, LL.D., F.R.S., Pres.G.S 1016 7. On certain Diatomaceous Deposits (Diatomite) from the Peat of Aber- deenshire. By W. Iyison Macadam, F.G.S., F.I.G 1017 8. List of Works on the Geology, Mineralogy, and Palaeontology of Stafford- shire, Worcestershire, and Warwickshire. Bv W. Whitaker, B.A., F.G.S., AssocInst.O.E '. 1017 FRIDAT, SEPTEMBER IL 1. The Volcanoes of Auvergne. By Tempest Anderson, M.D., B.Sc 1017 2. On the Re-discovery of lost Numidiaii Marbles in Algeria and Tunis. By Lieut.-Colonel R. L. Platfair 1018 3. Second Report on the Rate of Erosion of the Sea-coasts of England and Wales 1018 4. The Chasm called the Black Rock of Kiltearn. By William Watson 1018 5. The Bass of Inverurie, a fragment of an ancient Alluvial Bed. By the Rev. John Davidson, D.D 1018 6. Thirteenth Report on the Erratic Blocks of England, Wales, and Ireland 1019 7. The Direction of Glaci;ition as ascertained by the Form of the Striae. By Professor H. Carvill Lewis 1019 8. Proposed Conditions to account for a former Glacial Period in Great Britain, existing under similar meteorological conditions to those that rule at the present time. By W. F. Stanley, F.G.S., F.R.M.S 1020 9. On the Fyunon Beuno and Cae Gwyn Bone-Caves, North Wales. By H. Hicks, M.D., F.R.S., F.G.S 1021 10. Note on Specimens of Fish from the Lower Old Red Sandstone of For- farshire. By the Rev. Hugh Mitchell 1023 SATURDAY, SEPTEMBER 12. 1. The Elgin Sandstones. By J. Gordon Phillips 1023 2. Preliminary Note on a new Fossil Reptile recently discovered at New Spy nie, near Elgin. By Dr. R. H. Tkaquaik, F.R.S 1024 3. Report on the Fossil Plants of tbe Tertiary and Secondary Beds of the United Kingdom 1025 MONDAY, SEPTEMBER 14. 1. The Highland Controversy in British Geology: its Causes, Course, and Consequences. By Professor Charles Lapworth, LL.D., F.G.S 1025 2. The Geology of Durness and Eriboll, with special reference to the High- land Controversy. By B. N. Peach, F.R.S.E., and J. Horne, F.R.S. E. 1027 -3. Preliminary Note on some Traverses of the Crystalline District of the Central Alps. By Professor T. G. Bonnet, D.Sc, LL.D., F.R.S., Pres. G.S 1027 xvi CONTENTS. Page 4. Some Examples of Pressure-Fluxion in Pennsylvania. By Professor H. Cakvlll Lewis 1029 5. On Slaty Cleavage and allied Rock Structures, with special reference to the Mechanical Theories of their Origin. By Alfred Haeker, M.A., F.G.S 1030 6. On Irish Metamorphic Rocks. By G. Henry Kinahan, M.R.I.A lOSO' 7. On Rocks of Central Caithness. By John^ Gtjnn 1030 8. On some Rock Specimens from the Islands of the Fernando Noronha Group. By Professor A. Renabd, LL.D., F.G.S 1031 9. On the Average Density of Meteorites compared with that of the Earth. By the Rev. E. Hill, M.A., F.G.S 1031 TUESDAY, SEPTEMBER 15. 1. Notes on a recent Examination of the Geology of East Central Africa. By Professor Henrt Drummond, F.R.S.E., F.G.S 1032' 2. Report on the Rocks collected by H. "W. Johnston, Esq., from the upper part of the Kilima-njaro Massiif. By Professor T. G. Boxnet, D.Sc, LL.D., F.R.S., Pres.G.S 1032 3. Some Results of the CrystaUographic Study of Danburite. By Max Schuster '. 1033 4. American Evidences of Eocene Mammals of the ' Plastic Clay ' Period. By Sir Richard Owex, K.0.B.,F.R.S., F.G.S 1033 5. Discovery of Anurous Amphibia in the Jurassic Deposits of America. By Professor 0. C. Marsh 1033 6. Third Report on the Fossil Phyllopoda of the Palaeozoic Rocks 1033 7. On the Distribution of Fossil Fishes in the Estuariue Beds of the Carboniferous Formation. By Dr. Traquair 1033 8. Some Results of a detailed Sur^-ey of the Old Coast-lines near Trondh- jem, Norway. By Hugh Miller, F.G.S 1033 9. The Parallel Roads of Lochaber. By James Melvin 1035 10. Further Evidence of the Extension of the Ice in the North Sea during the Glacial Period. By B. N. Peach, F.R.S.E., and J. Horne, F.R.S.E.... 103(> 11. Recent Advances in West Lothian Geology. By H. M. Cadell, B.Sc. 1037 12. Barium Sulphate as a Cementing Material in Sandstone. By Professor Frank Clowes, D.Sc ". 1038 13. Notes on Fuller's Earth and its applications. By A. C. G. Cameron ... 1039 WEDNESDAY, SEPTEMBER 16. 1. On the Glacial Deposits at Montrose. By Dr. Howden 1040 2. Notes on the Rocks of St. Kilda. By Alexander Ross, F.G.S 1040 3. Eleventh Report on the Circulation of Underground Waters in the Per- meable Formations of England and AVales, and the Quantity and Character of the Water supplied to various Towns and Districts from these Formations 1041 4. On Deep Borings at Chatham : a Contribution to the Deep-seated Geology of the London Basin. By W. Whitaker,B.A., F.G.S., Assoc. Inst.C.E. 1041 5. On the Waterworks at Goldstone Road, Brighton. By W. Whitaker, B.A., F.G.S., Assoc.Inst.C.E " 1041 CONTENTS. XVll Section D.— BIOLOGY. THURSDAY, SEPTEMBER 10. Page Address by Professor W. 0. McIntosh, M.D., LL.D., F.R.S. L. & E., F.L.S., President of the Section 1043 1. On the Tay Whale {Megaptera longimana) and other Whales recently ohtained in the district. By Professor Strtjthers, M.D., LL.D 1053 2. Is the Commissural Theory of the Corpus Callosum correct ? By Pro- fessor D. J. Hamilton, M.B 1054 3. The Evidence of Comparative Anatomy with regard to Localisation of Function in the Cortex of the Brain. By Alex. Hill, M.A., M.B., M.R.O.S 1054 4. Report of the Committee for the Exploration of Kilima-njaro, and the adj oining Mountains of Eastern Equatorial Africa 1055 5. Report of the Committee for arranging for the occupation of a Table at the Zoological Station at Naples 1055 6. Report of the Committee for promoting the establishment of Marine Biological Stations on the coast of the United Kingdom 1056 7. Report of the Committee for promoting the establishment of a Marine Biological Station at Granton 1056 8. Report on recent Polyzoa 1056 9. Report on the Record of Zoological Literature 1056 10. Report on the Bibliography of certain Groups of Invertebrata 1056 FRIDAY, SEPTEMBER 11. 1. Recent Observations on the Habits and Instincts of Ants and Bees. By Sir John Lubbock, Bart., F.R.S 1056 2. On the Carpal Bones in various Cetaceans. By Professor Strtjthers, M.D., LL.D 1056 3. Account of the Dissection of the Rudimentary Hind-limb of Balcenoptera musculm. By Professor Strtjthers, M.D., LL.D 1056 4. Some points in the Anatomy of Sowerby's Whale (Mesoplodon bidens). By Professor W. Turner, M.B., F.R.S 1057 5. On the use of Graphic Representations of Life^histories in the teaching of Botany. By Professor F. 0. Bower 1057 Supplementary Meeting. — Physiology. 1. On the Direct Action of Anaesthetics on the Frog-heart. By J. McGregor-Robertson, M.A., M.B 1057 2. On the Action of Cold on Microphytes. By John G. McKendrick, M.D., LL.D., F.R.S .' 1058 3. On the Action of Ozonised Air upon Micro-Organisms and Albumen in Solution. By J. J. Coleman, F.C.S 1058 4. A new Theory of the Sense of Taste. By Professor J. Berry Haycraft 1059 SATURDAY, SEPTEMBER 12. 1. On a Model of the Whale. By Captam Gray 1059 2, On the Hybridisation of Salmonidae at Howietoun. By Francis Day, CLE 1059 1885. 0, ■xviii CONTENTS. Page 3, On the Identification of the British Mosses by their Distinctive Cha- racters. B}^ Mrs. FAEatTHAESON, F.R.M.S 106?. 4. On the Flora of Caithness. By James F. Grant 1063 .5. On Chinese Insect White Wax. By A. Hosie 1064 6. On the Existence of Cephalopoda in the Deep Sea. By W. E. Hoyle... 1064 7. On the Echiuoderm Fauna of the Island of Ceylon. By Professor F. Jeffrey Bell, M.A., Sec.R.M.S '. 1065 MONDAY, SEPTEMBER 14. 1. Report on the Aid given by the Dominion Government and the Govern- ment of the United States to the encouragement of Fisheries, and to the investigation of the various forms of Marine Life on the coasts and rivers of North America 1065 2. On the Size of the Brain in Extinct Animals. By Professor 0. C. Marsh 1065 3. On the Systematic Position of the Chamseleon, and its Affinities with the Dinosauria. By Professor D'Aecy W. Thompson 1065 4. On the Hind Limb of Ichthyosaurus, and on the Morphology of Verte- brate Appendages. By Professor DArcy W. Thompson 1065 5 On the Origin of the Fishes of the Sea of Galilee. Bv Professor Edward Hull, LL.D.,F.R.S ." 1066 Q, On the Cause of the Extreme Dissimilarity of the Faunas of the Red Sea and Mediterranean. By Professor Edward Hull, LL.D., F.R.S 1068 7 On the Morphology of the Human Arterial System. Bv Professor A. MacAlister, F.R.S " 1068 8. On the Viscera of Gymnotus electricus. By Professor Cleland, M.D., F.R.S 1068 9. On the Spiracle of Fishes in its relation to the Head, as developed in the Higher Vertebrates. By Profe.«sor Cleland, M.D., F.R.S 1069 10. On the Tail of Myxine glutinosa. By Professor Cleland, M.D., F.R.S. 1069 11. On the Nucleus in the Frog's Ovum. By George Thin, M.D 1069 12. On the Structure and Arrangements of the St. Andrews Marine Laboratory. By Professor McInxosh, M.D., LL.D., F.R.S 1071 13. Remarks on the work at the St. Andrews Marine Laboratory during nine months. By Professor McIntosh, M.D., LL.D., F.R.S 1071 14 On the Chemical Composition of the Milk of the Porpoise. Bv Professor PuRDiE, Ph.D., B.Sc '. 1072 15. On certain processes formed bv Oerapus on Tubulana indivisa. By Professor McIntosh, M.D., LL.D., F.R.S .'. 1072 16. On a new British Staurocephalus. By Professor McIntosh, M.D., F.R.S. 1073 17. On certain remarkable Structures resembling Ova from Deep Water. By Professor McIntosh, M.D., LL.D., F.R.S 1073 18. On the Ova of Callionymus lyra, L. (the Skulpin). By Professor McIntosh, M.D., LL.D., F.R.S 1073 19. On the Zoocytium or Gelatinous Matrix of Ophrydium versatile. By Professor Allen Haeker, F.L.S 1074 Supplementary Meeting. — Physiology. 1. On the Action of Atropine on the Secretion of the Kidney, its Evidence as to the Mechanism of the Secretion. By J. McGregor-Robertson, M.A.,M.B 1075 CONTENTS. xix Page 2. On a Chemical Difference between Living and Dead Protoplasm. By Oscar Loew, Ph.D 1075 3. A Comparative View of the Albuminous Substances contained in the Blood of Vertebrate and Invertebrate Animals. By W. D. Halli- BUETON, M.D., B.Sc, M.R.C.P 1077 4. On the Striated Muscles in the Gills of Fishes. By Dr. J. A. McWiLLIAM 1077 5. On the Structm-e of the Intestine in the Hedgehog and the Mole. By Dr. J. A. McWiLLiAM 1078 6. On Plant-Digestion, especially as occurring in Carica papaya. By Sidney MARim, M.D., B.Sc, M.E.C.P 1078 7. On a new kind of Colour Apparatus for Physiological Experiment. By John Aiken 1079 8. On the Structure of Hyaline Cartilage. By Geoege Thin, M.D 1078 9. The Preservation and Prolongation of Life to 100 years. By Protheeoe Smith, M.D 1079 SUPPLEMENTAET MEETING. — BOTANT. 1. On the Application of the Anatomical Method to the Determination of the Materials of the Linnean and other Herbaria. By Professor L. Radlkofer 1080 2. On the Influence of Impregnation on a Plant. By E. J, Lowe, F.R.S.... 1081 3. On the Impregnation of Composite Flowers. By E. J. Lowe, F.R.S. ... 1082 4. On the Occurrence of Fungi in the Roots of Orchids. By J. Macmillan 1083 5. Notes on Experiments as to the Formation of Starch in Plants under the influence of the Electric Light. By H. Marshall Ward 1086 6. On the Flora of Banfishire. By the Rev. W. S. Bruce 1087 7. On the Flora of Elgin. By James Mackenzie 1087 8. On the Division and Conjugation of Spirogyra. By Dr. J. M. Macfar- LANE, F.R.S.E ". 1088 9. On a Microscopic Fungus in Fossil Wood, from Bowling. By Dr. J. M. Macfarlane, F.R.S.E 1088 10. On a new Method of preparing the Epidermal Tissues of Pitcher Plants. By Dr. J. M. Macfarlane, F.R.S.E 1088 11. On Aberdeenshire Plants as Food for Animals. By William Wilson, jun 1088 TUESDAY, SEPTEMBEE 15. 1. Report on the Migration of Birds 1089 "2. Note on the Intelligence of the Dog. By Sir John Lttbbock, Bart., F.R.S. 1089 3. On the Development of the Food-fishes at the St. Andrews Marine Laboratory. By Edward E. Prince 1091 4, On the Nest and Development of Gastrosteus gpinachia at the St. An- drews Marine Laboratory. By Edward E. Prince 1093 .5. On the Reproduction of the Common Mussel (Myttlus ediUis, L.) By John Wilson IO94 6. On the Modification of the Trochal Disc of the Rotifera. By Professor A. G. Bourne, D.Sc, F.L.S - IO95 a 2 XX CONTENTS. Page 7. On Buddine- in the OligocliEeta. By Professor A. G. Bofene, D.Sc, F.L.S 109G 8. Demonstration of a new Moneron. By Professor D'Arcy W. Thompsoi^ 1097 9. On the Blastopore and MesoUast of Sabella. By Professor D'Arct W. Thompson 1097 10. On the Annelids of the Genus Dero. By E. C. Botjsfield 1097 11. On some little known Fresh-water Annelids. By E. C. Bousfield 1098 12. On the Coloration of the Anterior Segments in the Malanidse. By Pro- fessor Allen II.VKKER, F.L.S 1098 1.3. Systematique du genre Polygordius. By Julien Fraipont 1098 14. On some of our Migratory Birds, as first seen in Aberdeenshire. By James Taylor 1098 Supplementary Meeting. — Anatomy. 1. On the Connection of the Os Odontoidium with the centrum of the axis vertebra. By Professor D. J. Cunningham, F.R.S 1101 2. On the Curvature of the Spine in the Foetus and Child. By Dr. John- ston Symington 1101 3. On the Bronchial Syrinx of the Cuculidse and Caprimulgidse. By Frank E. Beddard, M.A., F.R.S.E 1101 4. Contributions to the Structure of the Oligochseta. By Frank E. Bed- dard, M.A., F.R.S.E 110^ 5. On the Cervical Vertebrae in Balaina mysticetus, &c. By Professor Struthers, M.D., LL.D 1103 6. On the Development of the Foot of the Horse. By Professor Struthers, M.D., LL.D '. llOa 7. On the Development of the Vertebraj of the Elephant. By Professor Struthers, M.D., LL.D 110^ 8. On the Kidneys of Gasteropoda and the Renal Duct of Paludina. By W. B. Benham 1103- Section E.— GEOGRAPHY. TIIUR.SDAY, SEPTEMBER 10. 1. The Indian Forest School. By Major F. Bailey, R.E., F.R.G.S 1104 2. Brazil. By Colin Mackenzie, F.R.G.S 1105 3. On the Progress of African Philology. By R. Needham Cust, F.R.G.S '. ". 1105 4. On the Changes which have taken place in Tunis since the French Pro- tectorate. By Lieut.-Colonel R. L. Playfaie 1105 FRIDAY, SEPTEMBER IL Address by General J. T. Walker, C.B., R.E., LL.D., F.R.S., President of the Section HOC? 1. The Indian Forest Survey. By Major F. Bailey, R.E., F.R.G.S 1121 2. Account of the Levelling Operations of the Great Trigonometrical Survey of India. By Major A. W. Baied, R.E., F.R.S 112.3 3. Notes on the Physiography of Southern India. By Colonel B. R. Bkanfill 112-1 CONTENTS. XXI Page 4. On a Trip from Upper Assam into the Kampti Country and the Western Branch of the Irrawady River, made by Colonel R. B. AVoodthorpe, R.E., and Major C. R. MacGregor. By Lieut.-Colonel H. H. Qodwin- Adsten, F.R.S 1126 5. On the complete Exploration of Lake Yamdok in Tibet. By Tee- LAWNEX SaUNDEES 1126 <3. On Himalayan Snow Peaks. By Lieut.-Colonel H. C. B. Taiinbr 1126 7. Notes on recent Mountaineering in the Himalaya. By Douglas AV. Feeshfield, F.R.G.S 1127 MONDAY, SEPTEMBER 14. 1. Projected Restoration of the Reian Moeris, and the Province, Lake, and Canals ascribed to the Patriarch Joseph. By Cope Whitehouse, M.A. 1127 2. Report of the Committee for furthering the Scientific Examination of the Country in the vicinity of Mount Roraima in Guiana 1128 3. Mount Roraima. By Eveeard iii Thuen 1128 4. Report of the Committee appointed for the purpose of promoting the Survey of Palestine 1128 5. The Cadastral Survey of India. By Lieut.-Colonel W, Barron 1128 6. The Ordnance Survey of Cyprus. By Teelawney Saunders 1129 7. The Rivers of the Punjab. By General Robert Maclaqan,R.E 1129 8. On a Clinometer to use vdth a Plane-Table. By Major Hill 1131 9. On a supposed Periodicity of the Cyclones of the Indian Ocean, south of the Equator 1131 10. The Portuguese Possessions in West Africa. By H. H. Johnston 1132 11. North-west Australia, By J. G. Bartholomew 1132 TUESDAY, SEPTEMBER 15. 1. Antarctic Research. By Admiral Sir Erasmus OMMANNEr,C.B., F.R.S., F.R.G.S 1132 2. Geogiaphical Education. By J. Scott Kelxie 1133 3. On Overland Expeditions to the Arctic Coast of America. By John Rae, M.D., LL.D., F.R.S., F.R.G.S 1133 4. On the best and safest Route by which to attain a High Northern Latitude. By John Rae, M.D., LL.D., F.R.S., F.R.G.S 1136 5. Oceanic Islands and Shoals. By J. Y. Buchanan 1136 6. On the Depth of the permanently Frozen Stratum of Soil in British North America. By General Sir J. Henet Lefeot, K.C.M.G., F.R.S. 1136 7. On Recent Explorations in New Guinea. By Coutts Teotter 1136 WEDNESDAY, SEPTEMBER 16. 1. On Journeyings in South-western China. By A. Hosie 1137 2. Notes on the large Southern Tributaries of the Rio Solimoes or Upper Amazon in Brazil, with special reference to the Rio Jutahi. By Pro- fessor J. W. H. Teail 1138 3. The Depth and Temperature of some Scottish Lakes. By J. Y. Buchanan 1138 XXll CONTENTS. Page 4. On the Geographical Features of the Beauly Basin. By Tho. W. Wallace ll;38- 5. What has been done for the Geography of Scotland, and what remams to he done. By H. A. Websteb 1138- 6. On Bathy-hypsographical Maps, with special reference to a Comhination of the Ordnance and Admiralty Surveys. By E. G. Eavenstein, F.K.G.S.. 1140 Section F.— ECONOMIC SCIENCE AND STATISTICS. THURSDAY, SEPTEMBER 10. 1. Report of the Committee for continuing the inquiries relating to the teaching of Science in Elementary Schools 1141 Address by Professor Henry Sidgwick, M.A., Litt.D., President of the Section 1141 2. On the alleged Depression of Trade. By Professor Leone Levi, F.S.S... 11 ')5 3. On the Variations of Price-Level since 1«50 By Michael G. IMulhall, F.S.S 1157 FRIDAT, SEPT EM BE It 11. 1. On the Municipalisation of the Land. By Sir George Campbell, K.CS.L, M.P 1158 2. The Agriculture of Aberdeenshire. By Colonel Innes 1161 3. The Agricultural Situation. By Professor W. Fream, B.Sc, F.L.S., F.G.S IIGI 4. On recent Changes in Scottish Agriculture. By Major P. G. Craigie.,. 11G2 SATURDAY, SEPTEMBER 12. 1. On the International Forestry Exhibition. By Dr. Ceombie Brown ... 1164 2. What is Capital ? By W. Westgarth 1165 3. On Methods of afcertainiug Variations in the Rates of Birth, Death, and Marriage. By F. Y. Edgeworth 1165 4. On the Application of Biology to Economics. By Patrick Geddes IIGG MONDAY, SEPTEMBER 14. 1. On the Use of Index Numbers in the Investigation of Trade Statistics. By Stephen Bourne, F.S.S 1168 2. On Depression of Prices and Results of Economy of Production, and on the Prospect of Recovery. By Hyde Clarke, F.S.S 1168 3. On Customs Tarifls. By A. E. Bateman 1160 4. How its Fiscal Policy may affect the Prosperity of a Nation. By Alexander Forbes 11 60 3. On the Incidence of Imperial Taxation. By Dr. W. A. Hunter 1170 TUESDAY, SEPTEMBER 15. 1. State Guarantee of War Risks. By John Corry 1171 2. On the British Standard of Value. By Dana Horton 1172 CONTENTS. XXm Page 3. Sliding Scales in the Coal Industry. By Professor J. E. C. Mttnro 1173 4. Anomalies in the condition of Scotch Miners in contrast with other un- skilled Labourers. By William Small 1174 6. The Statistics and some points in the Economics of the Scottish Fisheries. By William Wati, F.S.S 1175 6. On the Pauperisation of Children by the Operation of the ' Scotch Education Act, 1872.' By Matthew Blair 1176 WEDNESBAT, SEPTEMBER 16. 1. Agricultural Investigation and Education. By Thomas Jamieson 1177 2. Policy in Taxation. By J. B. Greig 1179 3. A new view of the Consequences of Unpunctuality in Railway Trains. By Cornelius Walford, F.I.A., F.S.S 1180. 4. On the Industrial Remuneration Conference. By the Rev. W. Cunningham, B.D 1181 Section G.— MECHANICAL SCIENCE. THURSBAY, SEPTEMBER 10. Address by B. Baker, M.Inst.C.E., President of the Section 1182 1. The New Tay Viaduct. By Crawford Barlow, B.A., M.Inst.C.E. ... 1192 2. The Forth Bridge Works. By Andrew S. Bjggart, C.E 1193 FRIBAY, SEPTEMBER 11. 1. The American System of Oil Pipe Lines. By J. H. Harris 1193 2. The Movement of Land in Aberdeen Bay. By W. Smith 1193 3. On Shallow-draught Screw Steamers for the Nile Expedition. By J. T. Thornycroft, M.Inst.C.E 1193 4. The Sphere and Roller Friction Gear. By Professor H. S. Hele Shaw 1193 5. On the Employment of the Road Engine in Construction and Main- tenance of Roads. By Colonel Innes 1194 MOXBAY, SEPTEMBER 14. 1. Electric Lighting and the Law. By Dr. Leavis Edmunds 1195 2. On an Electric Safety Lamp for Miners. By J. Wilson Swan, M.A.... 1196 3. On the Strength of Telegraph Poles. By W. H. Preece, F.R.S., M.Inst.C.E 1197 4. On Domestic Electric Lighting. By W. H. Preece, F.R.S., M.Inst.C.E. 1197 5. On a System of Periodic Clock Control on Telephone or Telegraph Lines. By Professor W. F. Barrett, F.R.S.E 1198 6. Electric Lighting at the Forth Bridge Works. By James N, Shool- bred, B.A., M.Inst.C.E 1198 7. On the Development of the Pneumatic System as applied to Telegraph purposes. By J. W. Willmot 1198 TTTESBAY, SEPTEMBER 15. 1. Report of the Patent Law Committee 1199 2. Autographic Apparatus for Machines for Testing Materials. By Pro- fessor W. C. Unwin, M.Inst.C.E 1199 XXIV CONTENTS. Page 3. Notes on Mild Steel. ByG.J. Goedon 1200 4. The Diminution of Casualties at Sea. By Don Artfko de Maecoakttj 1201 5. On the Deep Sea Channel into Swansea Harbour. By Robert Oappek 1202 6. On the Spey Bridge at Garmouth and the River Spey. By P. M. Baenett 1203 7. On a New Form of High Speed Friction Driving Gear. By Professor J. A. EwiNG ; 1203 8. On Ashton's New Power Meter. By Professor H. S. Hele Shaw 1203 9. On the British Association Standard Gauge for Small Screws. By Edwaed Rigg, M.A 1203 Section H.— ANTHROPOLOGY. THURSDAY, SEPTEMBER 10. 1. The Scope of Anthropology, and its relation to the Science of Mind. By Alexander Bain, LL.D 1204 2. The Index of the Pelvic Brim as a Basis of Classification. By Professor W. TuENER, M.B., F.R.S 1205 3. A Portable Scale of Proportions of the Human Body. By W. F. Stanley, F.G.S., F.K.M.S 1206 Address by Francis Galton, M.A., F.R.S., President of the Anthropo- logical Institute, President of the Section 1206 FRIDAY, SEPTEMBER 11. 1. Insular Greek Customs. By J. Theodore Bent 1214 2. On the Working of the Ancient Monuments Act of 1882. By General PiTT-RivERs, r.R.S 1214 3. American Shell-work and its Affinities. By Miss A. W. Buckland ...1214 4. Note on the Redmen about Roraima. By E. F. im Thtten 1215 5. A Game with a History. By J. W. Crombie, M.A 1215 6. The Rule of the Road from an Anthropological point of view. By Sir George Campbell, K.O.S.I 1215 7. On the Modes of Grinding and Drying Corn in old times. By Miss Jeanie M. Laing 1216 8. The Flint-knappers' Art in Albania. By A. J. Evans 1216 9. The Discovery of Nauki-atis. By W. M. Flinders Petrie 1216 MONDAY, SEPTEMBER 4. 1. On Ancient Tombs in the Greek Islands. By J. Theodore Bent 1217 2. A New Cave Man of Mentone. By Thomas Wilson 1218 3. Happaway Cavern, Torquay. By William Pengellt, F.R.S., F.G.S. , 1219 4. On the Human Remains found in Happaway Cavern, Torquav. By J. G. gaeson, m.d :. ....•; ;; 1220 5. On Three Stone Circles in Cumberland, with some further observations on the relation of Stone Circles to adjacent hills and outlying stones. By A. L. Lewis, M.A.I ...Tf. 1220 CONTENTS. XXV Page 6. The Archaeological Importance of ancient British Lake-dwellings and their relation to analogous remains in Europe. By R. Munko, M.A., M.D 1221 7. The Stone Circles in Aherdeenshire, -with special reference to those in the more Lowland parts of the County, their Extent and Arrangement, singly or in gi-oups, with General Observations. By the Rev. James Peter, F.S.A.Scot '. 1221 8. Stone Circles in Aberdeenshire. By John Mtlne, M.A 1223 9. Notes on a recent Antiquarian Find in Aberdeenshire. By Dr. F. Mait- LAND MoiB 1223 10. The Picts and Prje-Celtic Britain. By Hyde Clarke 1223 11. Report of the Committee for investigating and publishing reports on the physical characters, languages, and industrial and social condi- tions of the North-western Tribes of the Dominion of Canada 1224 TUESDAY, SEPTEMBER 15. 1. Notes on the opening of a Cist in the parish of Leslie, Aberdeenshire. By the Rev. John Russeu, M.A 1224 2. Notes on a Cist found at Parkhill, Dyce, in October 1881. By W. Ferguson 1225 3. On the Human Crania and other contents found in short stone Cists in Aberdeenshire. By Professor J. Struthers, M.D., LL.D 1225 4. Notice of Human Bones found in 1884 in Balta Island, Shetland, by D. Edmonston, Esq. By Professor J. Struthers, M.D., LL.D 1225 6. Some Important Points of Comparison between the Chimpanzee and Man. By Professor D. J. Cunningham 1226 6. Abnormal and Arrested Development as an Indication of Evolutionary History. By J. G. Garson, M.D 1226 7. The Symbol Pillars abounding in Central Aberdeenshire. Bv the Rev. John Davidson, D.D .* 1227 8. Notes on some of the Bantu Tribes living round Lake Nyasa in Eastern Central Africa. By Dr. Robert Laws 1227 9. Exhibition of the Skeleton of a Strandlouper from South Africa. By Professor A. Macalister, F.R.S 1228 10. A brief Account of the Nicobar Islanders, with .special reference to the Inland Tribe of Great Nicobar. By E. H. Man 1228 11. A proposed Society for Experimental Psychology. By Joseph Jacobs, B.A : 1230 12. A Comparative Estimate of Jewish Ability. By Joseph Jacobs, B.A.... 1231 13. Traces of Early Human Habitations on Deeside and Vicinity. By the Rev. J. G. Michie, A.M 1232 Index 1233 XXVI LIST OF PLATES. LIST OF PLATES. PLATES I., IL, AND III. Illustrating the Eeport of the Committee on the Fossil Plants of tlie Tertiary andl Secondary Beds of the United Kingdom. PLATE IV. Illustrating the Report ot the Committee on the Erosion of the Sea-coasts of England and Wales. PLATES V. AND Va. Illustrating Mr. Meldrum's Communication, ' A Tabular Statement of the Dates at which, and the Localities where. Pumice or Volcanic Dust was seen in the Indian Ocean in 1883-84.' PLATE VI. Illustrating Mr. Andrew S. Biggart's Communication, ' The Forth Bridge Works.' PLATE VII. Illustrating Mr. Crawford Barlow's Communication, ' The New Tay Viaduct.' OBJECTS AND RULES OF THE ASSOCIATION. OBJECTS. The Association contemplates no interference with the ground occupiedl by other institutions. Its objects are : — To give a stronger impulse and a more systematic direction to scientific inquiry, — to promote the inter- course of those who cultivate Science in different parts of the British Empire, with one another and with foreign philosophers, — to obtain a more general attention to the objects of Science, and a removal of any disadvantages of a public kind which impede its progress. RULES. Admission of Members and Associates. All persons who have attended the first Meeting shall be entitled to become Members of the Association, upon subscribing an obligation to conform to its Rules. The Fellows and Members of Chartered Literary and Philosophical Societies publishing Transactions, in the British Empire, shall be entitled,, in like manner, to become Members of the Association. The Officers and Members of the Councils, or Managing Committees, of Philosophical Institutions shall be entitled, in like manner, to become Members of the Association. All Members of a Philosophical Institution recommended by its Coun- cil or Managing Committee shall be entitled, in like manner, to become Members of the Association. Persons not belonging to such Institutions shall be elected by the- General Committee or Council, to become Life Members of the Associa- tion, Annual Subscribers, or Associates for the year, subject to the approval of a General Meeting. Compositions, Subscriptions, and Privileges. Life Members shall pay, on admission, the sum of Ten Pounds. They shall receive gratuitously the Reports of the Association which may be published after the date of such payment. They are eligible to all the offices of the Association. Annual Subscribers shall pay, on admission, the sum of Two Pounds, and in each following year the sum of One Pound. They shall receive gratuitously the Reports of the Association for the year of their admission and for the years in which they continue to pay without intermission their Annual Subscription. By omitting to pay this subscription in any par- ticular year, Members of this class (Annual Subscribers) Insp for that and iXVlU RULES OF THE ASSOCIATION. all future years tlie privilege of receiving the volumes of the Association gratis : but they may resume their Membership and other privileges at any subsequent Meeting of the Association, paying on each such occasion the sum of One Pound. They are eligible to all the Offices of the Asso- •ciation. Associates for the year shall pay on admission the sum of One Pound. They shall not receive gratuitously the Reports of the Association, nor be eligible to serve on Committees, or to hold any office. The Association consists of the following classes : — 1. Life Members admitted from 1831 to 1845 inclusive, who have paid on admission Five Pounds as a composition. 2. Life Members who in 1846, or in subsequent years, have paid on admission Ten Pounds as a composition. 3. Annual Members admitted from 1831 to 1839 inclusive, subject to the payment of One Pound annually. [May resume their Membership after intermission of Annual Payment.] 4. Annual Members admitted in any year since 1839, subject to the payment of Two Pounds for the first year, and One Pound in each ifollowing year. [May resume their Membership after intermission of Annual Payment.] 5. Associates for the year, subject to the payment of One Pound. 6. Corresponding Members nominated by the Council. And the Members and Associates will be entitled to receive the annual volume of Reports, gratis, or to 2^^^'''<^^>(^-^^ it at reduced (or Members') •price, according to the following specification, viz. : — 1. Gratis. — Old Life Members who have paid Five Pounds as a com- position for Annual Payments, and previous to 1845 a fur- ther sum of Two Pounds as a Book Subscription, or, since 1845, a further sum of Five Pounds, New Life Members who have paid Ten Pounds as a compo- sition. Annual Members who have not intermitted their Annual Sub- scription. 2. At reduced or Memhers" Prices, viz. two-thirds of the Publi- cation Price. — Old Life Members who have paid Five Pounds as a composition for Annual Payments, but no further sum as a Book Subscription. Annual Members who have intermitted their Annual Sub- scription. Associates for the year. [Privilege confined to the volume for that year only.] 3. Members may purchase (for the purpose of completing their sets) any of the volumes of the Reports of the Association up to 1874, of lohich more than 15 copies remain, at 2s. 6c?. per volume. • Application to be made at the Office of the Association, 22 Albemarle Sti-eet, London, W. Volumes not claimed within two years of the date of publication can •only be issued by direction of the Council. Subscriptions shall be received by the Treasurer or Secretaries. ' A few complete sets, 1831 to 1874, are on sale, £10 the set. RULES OF THE ASSOCIATION. XXIX Meetings. The Association shall meet annually, for one week, or longer. The- place of each Meeting shall be appointed bj^ the General Committee two years in advance ; and the arrangements for it shall be entrusted to the Officers of the Association. General Committee. The General Committee shall sit during the week of the Meeting, or longer, to transact the business of the Association. It shall consist of the following persons : — Class A. Peejiaxent Members. 1. Members of the Council, Presidents of the Association, and Presi- dents of Sections for the present and preceding years, with Authors of Reports in the Transactions of the Association. 2. Members who by the publication of Works or Papers have fur- thered the advancement of those subjects which are taken into considei-a- tion at the Sectional Meetings of the Association. With a view of sub- mitting neio claims under this Rule to the decision of the Council, they must be sent to the Secretary at least one month before the Meeting of the Association. The decision of the Council on the claims of any Member of the Association to be placed on the list of the General Committee to be final. Class B. Temporary Members.' 1. Delegates nominated by the Corresponding Societies under the conditions hereinafter explained. Claims under this Rule to be sent to the Secretary before the opening of the Meeting. 2. Office-bearers for the time being, or delegates, altogether not ex- ceeding three, from Scientific Institutions established in the place of Meeting. Claims under this Rule to be approved by the Local Secretaries before the opening of the Meeting. 3. Foreigners and other individuals whose assistance is desired, and who are specially nominated in writing, for the Meeting of the year, by the President and General Secretaries. 4. Vice-Presidents and Secretaries of Sections. Organizing Sectional Committees.^ The Presidents, Vice-Presidents, and Secretaries of the several Sec- tions are nominated by the Council, and have power to act until their names are submitted to the General Committee for election. From the time of their nomination they constitute Organizing Com- mittees for the purpose of obtaining information upon the Memoirs and Reports likely to be submitted to the Sections,^ and of preparing Reports thereon, and on the order in which it is desirable that they should be read, to be presented to the Committees of the Sections at their first ' Revised by the General Committee, 188i. - Passed by the General Committee, Edinburgh, 1871. ' Kofict' to Contribtitoi-s of Memoirs. — Authors are reminded that, under an arrangement dating from 1871, the acceptance of Memoirs, and tlie days on which they are to be read, are now as far as possible determined by Organizing Committees for the several Sections before the hef/inninr/ of the Meeting. It has therefore become necessary, in order to give an opportunity to the Committees of doing justice to the several Communications, that each Author should prepare an Abstraci'of his Memoir, of a length suitable for insertion in tJie published Transactions of the Association, and that he should send it, together with the original Memoir, by book-post, on or XXX RULES OF THE ASSOCIATION. meeting. The Sectional Presidents of former years are ex ojjicio members of the Organizing Sectional Committees.' An Organizing Committee may also hold such preliminary meetings as the President of the Committee thinks expedient, but shall, under any circumstances, meet on the first Wednesday of the Annual Meeting, at 11 A.M., to nominate the first members of the Sectional Committee, if they shall consider it expedient to do so, and to settle the terms of their report to the General Committee, after -which their functions as an Organizing Committee shall cease. ^ Constitution of the Sectional Comviittees.^ On the first day of the Annual Meeting, the President, Vice-Presi- dents, and Secretaries of each Section having been appointed by the General Committee, these Officers, and those previous Presidents and Vice-Presidents of the Section who may desire to attend, are to meet, at 2 P.M., in their Committee Rooms, and enlarge the Sectional Committees by selecting individuals from among the Members (not Associates) present at the Meeting whose assistance they may particularly desire. The Sec- tional Committees thus constituted shall have power to add to their number from day to day. The List thus formed is to be entered daily in the Sectional Minute- Book, and a copy forwarded without delay to the Printei-, who is charged with publishing the same before 8 A.M. on the next day in the Journal of the Sectional Proceedings. Business of the Sectional Comviittees. Committee Meetings are to be held on the Wednesday at 2 p.m., on the following Thursday, Friday, Saturday,^ Monday, and Tuesday, from 10 to 11 A.M., punctually, for the objects stated in the Rules of the Association, and specified below. The business is to be conducted in the following manner : — 1. The President shall call on the Secretary to read the minutes of the previous Meeting of the Committee. 2. No paper shall be read until it has been formally accepted by the Committee of the Section, and entered on the minutes accord- ingly. 3. Papers which have been reported on unfavourably by the Organiz- ing Committees shall not be brought before the Sectional Committees.® At the first meeting, one of the Secretaries will read the Minutes of last year's proceedings, as recorded in the Minute-Book, and the Synopsis before , addressed thus — 'General Secretaries, British Associa- tion, 22 Albemarle Street, London, W. For Section ' If it should be incon- venient to the Author that his paper should be read on any particular days, he is requested to send information thereof to the Secretaries in a separate note. Authors who send in their MSS. three complete weeks before the Meeting, and whose papers are accepted, will be furnished, before the Meeting, with printed copies of their Eeports and Abstracts. No Report, Paper, or Abstract can be inserted in the Annual Volume unless it is handed either to the Recorder of the Section or to the Secretary, ■be/ore the conclusion of the Mcetin/f. ' Added by the General Committee, Sheffield, 1879. 2 Revised by the General Committee, Swansea, 1880. ' Passed by the General Committee, Edinburgh, 1871. * The meeting on Saturday was made optional by the General Committee at Pouthport, 1883. ' These rules were adopted by the General Committee, Plymouth, 1877. KOLES OF THE ASSOCIATION. XXXI of Recommendatious adopted at the last Meeting of the Association and printed in the last volume of the Transactions. He will next proceed to read the Report of the Organizing Committee.' The list of Communi- cations to be read on Thursday shall be then arranged, and the general distribution of business throughout the week shall be provisionally ap- pointed. At the close of the Committee Meeting the Secretaries shall forward to the Printer a List of the Papers appointed to be read. The Printer is charged vidth publishing the same before 8 A.M. on Thursday in the Journal. On the second day of the Annual Meeting, and the follovring days, the Secretaries are to correct, on a copy of the Joui-nal, the list of papers which have been read on that day, to add to it a list of those appointed to be read on the next day, and to send this copy of the Journal as early in the day as possible to the Printer, who is charged with printing the same before 8 a.m. next morning in the Journal. It is necessary that one of the Secretaries of each Section (generally the Recorder) should call at the Printing Office and revise the proof each evening. Minutes of the proceedings of every Committee are to be entered daily in the Minute-Book, which should be confirmed at the next meeting of the Committee. Lists of the Reports and Memoirs read in the Sections are to be entered in the ^linute-Book daily, which, with all Memoirs and Copies 07- Abstracts of Memoirs furnished hy Autlwrs, are to hefonvarded, at the close of the Sec- tional Meetings, to the Secretary. The Vice-Presidents and Secretaries of Sections become ex officio tem- porary Members of the General Committee (vide'p. xxix), and will receive on application to the Treasurer in the Reception Room, Tickets entitling them to attend its Meetings. The Committees will take into consideration any suggestions which may be offered by their Members for the advancement of Science. They are specially requested to review the recommendations adopted at preceding Meetings, as published in the volumes of the Association and the com- munications made to the Sections at this Meeting, for the purposes of selecting definite points of research to which individual or combined exertion may be usefully directed, and branches of knowledge on the state and progress of which Reports are wanted ; to name individuals or Com- mittees for the execution of such Reports or researches ; and to state whether, and to what degree, these objects may be usefully advanced by +he appropriation of the funds of the Association, by application to Government, Philosophical Institutions, or Local Authorities. In case of appointment of Committees for special objects of Science it is expedient that all Members of the Committee shovld be named and one of them appointed to act as Secretary, for insuring attention to business. Committees have power to add to their number persons whose assist- ance they may require. The recommendations adopted by the Committees of Sections are to be registered in the Forms furnished to their Secretaries, and one Copy of each is to be forwarded, without delay, to the Secretary for presentation to the Committee of Recommendations. Unless this be done, the Eecom- mendations cannot receive the sanction of the Association. N.B. — Recommendations which may originate in any one of the Sec- tions must first be sanctioned by the Committee of that Section before they ' This and the following sentence were added by the General Committee 1871. xxxii KULES OF THE ASSOCIATION. can be referred to the Committee of Recommendations or confirmed by the General Committee. The Committees of the Sections shall ascertain whether a Report has been made by every Committee appointed at the previous Meeting to whom a sum of money has been granted, and shall report to the Committee of Recommendations in every case where no such Report has been received.' Notices regarding Ghxmts of Money. Committees and individuals, to whom grants of money have been entrusted by the Association for the prosecution of particular researches in science, are required to present to each following Meeting of the Association a Report of the progress which has been made ; and the Individual or the Member first named of a Committee to whom a money grant has been made must (previously to the next Meeting of the Associa- tion) forward to the General Secretaries or Treasurer a statement of the sums which have been expended, and the balance which remains dispos- able on each grant. Grants of money sanctioned at any one Meeting of the Association expire a lueek before the opening of the ensuing Meeting: nor is the Treasurer authorized, after that date, to allow any claims on account of such grants, unless they be renewed in the original or a modified form by the General Committee. No Committee shall raise money in the name or under the auspices of the British Association without special permission from the General Com- mittee to do so ; and no money so raised shall be expended except in accordance with the rules of the Association. In each Committee, the Member first named is the only person entitled to call on the Treasurer, Professor A. W. Williamson, University College, London, W.C, for such portion of the sums granted as may from time to time be required. In grants of money to Committees, the Association does not contem- plate the payment of personal expenses to the members. In all cases where additional grants of money are made for the con- tinuation of Researches at the cost of the Association, the sum named is deemed to include, as a part of the amount, whatever balance may remain unpaid on the former grant for the same object. All Instruments, Papei-s, Drawings, and other property of the Associa- tion are to be deposited at the OfiBlce of the Association, 22 Albemarle Street, Piccadilly, London, W., when not employed in carrying on scien- tific inquiries for the Association. Business of the Sections. The Meeting Room of each Section is opened for conversation from 10 to 11 daily. The Section Booms and approaches thereto can he used for no notices, exhibitions, or other purposes than those of the Association. At 11 precisely the Chair will be taken, ^ and the reading of communi- cations, in the order previously made public, commenced. At 3 p.m. the Sections will close. Sections may, by the desire of the Committees, divide them.3elves into Departments, as often as the number and nature of the communications delivered in may render such divisions desirable. ' Passed by the General Committee at Sheffield, 1879. - The meeting on Saturday may begin, if desired by the Committee, at any time not earlier than 10 or later than 11. Passed by the General Committee at Southport, 188.3. RULES OF THE ASSOCIATION. XXXm A Report presented to the Association, and read to the Section which originally called for it, may be read in another Section, at the request of the Officers of that Section, with the consent of the Author. Duties of the Doorkeepers. 1. — To remain constantly at the Doors of the Rooms to which they are appointed during the whole time for which they are engaged. 2. — To require of every person desirous of entering the Rooms the ex- hibition of a Member's, Associate's, or Lady's Ticket, or Reporter's Ticket, signed by the Treasurer, or a Special Ticket signed by the Secretary. 3. — Persons unprovided with any of these Tickets can only be admitted to any particular Room by order of the Secretary in that Room. No person is exempt from these Rules, except those Officers of the Association whose names are printed in the programme, p. 1. Duties of the Messengers. To remain constantly at the Rooms to which they are appointed dar- ing the whole time for which they are engaged, except when employed on messages by one of the Officers directing these Rooms. Committee of Recommendations. The General Committee shall appoint at each Meeting a Committee, which shall receive and consider the Recommendations of the Sectional Committees, and report to the Geneml Committee the measures which they would advise to be adopted for the advancement of Science. All Recommendations of Grants of Money, Requests for Special Re- searches, and Reports on Scientific Subjects shall be submitted to the Committee of Recommendations, and not taken into consideration by the General Committee unless previously recommended by the Committee of Recommendations. Ooo'responding Societies.^ (1.) Any Society is eligible to be placed on the List of Corresponding Societies of the Association which undertakes local scientific investiga- tions, and publishes notices of the results. (2.) Applications may be made by any Society to be placed on the List of Corresponding Societies. Application must be addressed to the Secretary on or before the 1st of June preceding the Annual Meeting at which it is intended they should be considered, and must be accompanied by specimens of the publications of the results of the local scientific investigations recently undertaken by the Society. (3.) A Corresponding Societies Committee shall be annually nomi- nated by the Council and appointed by the General Committee for the purpose of considering these applications, as well as for that of keeping themselves generally informed of the annual work of the Corresponding Societies, and of superintending the preparation of a list of the papers published by them. This Committee shall make an annual report to the General Committee, and shall suggest such additions or changes in the List of Corresponding Societies as they may think desirable. (4.) Every Corresponding Society shall return each year, on or before the 1st of June, to the Secretary of the Association, a schedule, ' Pas.serl by the General Committee, 1884. 1885. b -XXXiv RULES OP THE ASSOCIATION. properly filled np, which will be issued by the Secretary of the Associa- tion, and which will contain a request for such particulars with regard to the Society as may be required for the information of the Corresponding Societies Committee. (5.) There shall be inserted in the Annual Report of the Association a list, in an abbreviated form, of the papers published by the Corre- sponding Societies during the past twelve months which contain the results of the local scientific work conducted by them ; those papers only Taeing included which refer to subjects coming under the cognizance of one or other of the various Sections of the Association. (0.) A Corresponding Society shall have the right to nominate any one of its members, who is also a Member of the Association, as its dele- gate to the Annual Meeting of the Association, who shall be for the time a Member of the General Committee. Conference of Delegates of Corresponding Societies. (7.) The Delegates of the various Corresponding Societies shall con- stitute a Conference, of which the Chairman, Vice- Chairmen, and Secre- taries shall be annually nominated by the Council, and appointed by the General Committee, and of which the members of the Coi-responding Societies Committee shall be ex officio members. (8.) The Conference of Delegates shall be summoned by the Secretaries to hold one or more meetings during each Annual Meeting of the Associa- tion, and shall be empowered to invite any Member or Associate to take part in the meetings. (9.) The Secretaries of each Section shall be instructed to transmit to the Secretaries of the Conference of Delegates copies of any recommenda- tions forwarded by the Presidents of Sections to the Committee of Re- commendations bearing upon matters in which the co-operation of Corresponding Societies is desired ; and the Secretaries of the Conference of Delegates shall invite the authors of these recommendations to attend the meetings of the Conference and give verbal explanations of their objects and of the precise way in which they would desire to have them carried into efiect. (10.) It will be the duty of the Delegates to make themselves familiar with the purport of the several recommendations brought before the Confer- ence, in order that they and others who take part in the meetings may be able to bring those recommendations clearly and favourably before their respective Societies!. The Conference may also discuss propositions bear- ing on the promotion of more systematic observation and plans of opera- tion, and of greater uniformity in the mode of publishing I'esults. Local Cornmittees. Local Committees shall be formed by the Officers of the Association to assist in making arrangements for the Meetings. Local Committees shall have the power of adding to their numbers those Members of the Association whose assistance they may desire. Officers. A President, two or more Vice-Presidents, one or more Secretaries, and a Treasurer shall be annually appointed by the General Committee. RULES OF THE ASSOCIATION. XXXV Council. In the intervals of the Meetings, the affairs of the Association shall be managed by a Conncil appointed by the General Committee. The Council may also assemble for the despatch of business during the week of the Meeting. Papers and Communications. The Author of any paper or communication shall be at liberty to reserve his right of property therein. 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'00 OC53 fc*'^ 3 n r _•" Hc<i 2 CCp:;fi Sp5 1-3 Ecj m 6 cc pi 1-^ °s, S fe- te Hi CO : d : pj : fu '■ m '■ P5 '■ ^ : <=[^- .J -p; o .2 3 a; J . •3 S S -s R t» " S(2d -ci t" [ji. **-< ^J -3 - R-^r^ -f^ ^ C3 g r5 >>g c t3 H ^^^"^ oj 2 0) d'2 tc ^ ,13 x: M5 ^ 3 R r: -• - ."O o§§.3MO £KM| -^ D W W .-S "^ '^ 0.3 .3 i-l f- ^^ "1 S S .00 [CHE-i^PhPh CO • 6 ■ fe : CO • R • &; : CO • « : d rXi CO ^ R CO pi p-' R R R fi I?" -=J 1^ R - Rcq <iR^ *^ CO ^ c; pa COw p? p< fasw 3 > b*! WSo _« fli fl^ rt3 rf-i ^? Ms ago ^5 o ." — : ^^ .da : 1^* , Ca pJ ►^ k-H )- H d *r^ _,-r — .— * ^ "S to OS. < o -g- _0 l< S C3 « g^^ c -^ b< — o J3 & i? o •4^ , fi K 3 o ^ fe m 1-5 a t4 ■&.5Prt 5 i .a l"-. o HEH fo 1-3 PM „ 4) 4j o a) .2 3 a) OH tn £s a o . 2 Ph?H o 2 S o o H Eh '^f^-' hJPh-^ P p to to" cc.s • 1^1 : c« : i-i'' : rS CM 'Si ^ O 'r-* ^ U r,. f^ R « a> ■<1 ^ -g 3 ^-t-r- c ci t" : t- o Q<i|D K> a • S ; o M y p., tfc- r-l gtfi a, J P3b« O :S2 , K,a 1^ a a; ja H ph : a : « : D. : M : « : . •< -00 pH r.Q CO,- a !5 r« io» HJ W r aR .a PRESIDENTS AND SECRETARIES OF THE SECTIONS. xliii Presidents and Secretaries of the Sections of the Association. Date and Place Presidents Secretaries MATHEMATICAL AND PHYSICAL SCIENCES. COMMITTEE OF SCIENCES, I. — MATHEMATICS AND GENERAL PHYSICS. 1832. Oxford 1833. Cambridge Davies Gilbert, D.C.L., F.E.S. Sir D. Brewster, F.R.S. 1834. Edinburgh Rev. W. ^Vhewell, F.R.S. Rev. H. Coddington. Prof. Forbes. Prof. Forbes, Prof. Lloyd. 1835. Dublin 1836. Bristol 1837. Liverpool... 1838. Newcastle 1839. Birmingham 1840. Glasgow ... 1841. Plymouth 1842. Manchester SECTION A. — MATHEMATICS AND PHYSICS. Rev. Dr. Robinson 1843. Cork 1844. York 1845. Cambridge 1846. Southamp- ton. 1847. Oxford 1848. Swansea ... 1849. Birmingham 1850. Edinburgh 1851. Ipswich ... 1852. Belfast 1853. Hull 1854. Liverpool... 1855. Glasgow ... 1856. Cheltenham 1857. Dublin 1858. Leeds Rev. William WTiewell, F.R.S. Sir D. Brewster, F.R.S Sir J. F. W. Herschel, Bart., F.R.S. Rev. Prof . Whewell, F.R.S.... Prof. Forbes, F.R.S Rev. Prof. Lloyd, F.R.S Very Rev. G. Peacock, D.D., F R S Prof. M'Culloch, M.R.I. A. ... The Earl of Rosse, F.R.S. ... The Very Rev. the Dean of Ely. Sir John F. W. Herschel, Bart., F.R.S. Rev. Prof. Powell, M.A., F.R.S. Lord Wrottesley, F.R.S William Hopkins, F.R.S Prof. J. D. Forbes, F.E.S., Sec. R.S.E. Rev. W. Whewell, D.D., F.R.S. Prof. W. Thomson, M.A., F.R.S. L. & E. The Verj' Rev. the Dean of Ely, F.R.S. Prof. G. G. Stokes, M.A., Sec. E.S. Rev. Prof. Kelland, M.A., F.R.S. L. & E. Rev. R. Walker, M.A., F.R.S. Rev. T. R. Robinson, D.D., F.R.S., M.R.I.A. Rev. W. Whewell, D.D., V.P.R.S. Prof. Sir W. R. Hamilton, Prof. Wheatstone. Prof. Forbes, W. S. Harris, F. W. Jerrard. W. S. Harris, Rev. Prof. Powell, Prof. Stevelly. Rev. Prof. Chevallier, Major Sabine, Prof. Stevelly. J. D. Chance, W. Snow Harris, Prof. Stevelly. Rev. Dr. Forbes, Prof. Stevelly, Arch. Smith. Prof. Stevelly. Prof. M'Cuhoch, Prof. Stevelly, Rev. W. Scoresby. J. Nott, Prof .■ Stevelly. Rev. Wm. Hey, Prof. Stevelly. Rev. H. Goodwin, Prof. Stevelly, G. 6. Stokes. John Drew, Dr. Stevelly, G. G. Stokes. Rev. H. Price, Prof. Stevelly, G. G. Stokes. Dr. Stevelly, G. G. Stokes. Prof. Stevelly, G. G. Stokes, W. Eidout Wills. W. J.Macquorn Rankine, Prof .Smyth, Prof. Stevelly, Prof. G. G. Stokes. S. Jackson, W. J. Macquorn Rankine, Prof. Stevelly, Prof. G. G. Stokes. Prof. Dixon, W. J. Blacquorn Ran- kine, Prof. Stevelly, J. Tyndall. B. Blaydes Haworth, J. D. Sollitt, Prof. Stevelly, J. Welsh. J. Hartnup, H. G. Puckle, Prof. Stevelly, J. Tyndall, J. Welsh. Rev. Dr. Forbes, Prof. D.Gray, Prof. Tyndall. C. Brooke, Rev. T. A. Southwood, Prof. Stevelly, Rev. J. C. Turnbull. Prof. Curtis, Prof. Hennessy, P. A. Ninnis, W. J. Macquorn Rankine, Prof. Stevelly. Rev. S. Earnshaw, J. P. Hennessy, Prof. Stevelly, H.J. S.Smith, Prof. Tyndall. xliv REPORT — 1885. Date and Place 1859. Aberdeen... 1860. Oxford 1861. Manchester 1862. Cambridge 1863. Newcastle 1864. Bath 1865. Birmingham 1866. Nottingham 1867. Dundee ... 1868. Norwich ... 1869. Exeter 1870. Liverpool... 1871. Edinburgh 1872. Brighton... 1873. Bradford... 1874. Belfast 1875. Bristol 1876. Glasgow ... 1877. Plymouth... 1878. Dublin 1879. Sheffield ... 1880. Swansea ... 1881. York 1882. Southamp- ton. 1883. Southport 1884. Montreal ... 1885. Aberdeen... Presidents The Earl of Kosse, M.A., K.P., Rev. B. Price, M.A., F.E.S.... G. B. Airy, M.A., D.C.L., F.R.S. Prof. G. G. Stokes, M.A., F.R.S. Prof . W. J. Macquorn Rankine, C.E., F.R.S. Prof. Cayley, M.A., F.R.S., F.B.A.S. W. Spottiswoode,M.A.,F.R.S., F.R.A.S. Prof. Wheatstone, D.C.L., F.R.S. Prof. Sir W. Thomson, D.C.L., F.R.S. Prof. J. Tyndall, LL.D., F.R.S. Prof. J. J. Sylvester, LL.D., F.R.S. .J. Clerk Maxwell, M.A., LL.D., F.R.S. Prof. P. G. Tait, F.R.S.E. ... VV. De La Rue, D.C.L., F.R.S. Prof. H. J. S. Smith, F.R.S. Rev. Prof. J. H. Jellett, M.A.. M.R.I.A. Prof. Balfour Stewart, M.A., LL.D., F.R.S. Prof. Sir W. Thomson, M.A., D.C.L., F.R.S. Prof. G. C. Foster, B.A., F.R.S., Pres. Physical Soc. Rev. Prof. Salmon, D.D., D.C.L., F.R.S. Geortce Johnstone Stoney, M.A., F.R.S. Prof. W. Grylls Adams, M.A., F.R.S. Prof. Sir W. Thomson, M.A., LL.D., D.C.L., F.R.S. Rt. Hon. Prof. Lord Rayleigh, M.A., F.R.S. L'rof . 0. Heurici, Ph.D.,F.R.S., Prof. Sir W. Thomson, M.A., LL.D., D.C.L., F.R.S Prof. G. Chrystal, M.A., F.R.S.E. Secretaries J. P. Hennessy, Prof. Maxwell, H. J. S. Smith, Prof. Stevelly. Rev. G. C. Bell, Rev. T. Rennison, Prof. Stevelly. Prof. R. B. Clifton, Prof. H. J. S. Smith, Prof. Stevelly. Prof. R. B. Clifton, Prof. H. J. S. Smith, Prof. Stevelly. Rev.N.Ferrers,Prof.Fuller,F.Jenkin, Prof. Stevellv, Rev. C. T. Wiitley. Prof. Fuller, F. Jenkin, Rev. G. Buckle, Prof. Stevelly. Rev. T. N. Hutchinson, V. Jenkin, G. S. Mathews, Prof. H. J. S. Smith, J. M. Wilson. Fleeming Jenkin, Prof. H. J.S.Smith, Rev. S. N. Swann. Rev. G. Buckle, Prof. G. C. Foster, Prof. Fuller, Prof. Swan. Prof. G. C. Foster, Rev. R. Harley, R. B. Havward. Prof. G. C. Foster, R. B. Hay ward, W. K. Clifford. Prof. W. G. Adams, W. K. Clifford, Prof. G. C. Foster, Rev. W. Allen Whit worth. Prof. W. G. Adams, J. T. Bottomlev, Prof. W. K. Clifford, Prof. J. I). Everett, Rev. R. Harle)'. Prof. W.K. Clifford, .LW.L.Glaisher, Prof . A. S. Herschel, G. F. Rodwell. Prof. W. K. Clifford, Prof. Forbes, J. W.L. Glaisher, Prof. A. S. Herschel. J. W. L. Glai.sher, Prof. Herschel, Randal Nixon, J. Perry, G. F. Rodwell. Prof. W. F. Barrett, J. W.L. Glaisher, C. T. Hudson, G. F. Rodwell. Prof. W. F. liarrett, J. T. Bottomley, Prof. G. Forbes, J. W. L. Glaisher, T. Muir. Prof. W. F. Barrett, J. T. Bottomley, J. W. L. Glaisher, F. G. Landon. Prof. J. Casey, G. F. Fitzgerald, J. W. L. Glaisher, Dr. O. J. Lodge. A. H. Allen, J. W. L. Glaisher,''Dr. O. J. Lodge, D. MacAlister. W. E. Ayrtion, J. W. L. Glaisher, Dr. O. J. Lodge, D. MacAlister. Prof. W. E. Ayrton, Prof. O. J. Lodge, D. IMacAlister, Rev. W. Routh. W. M. Hicks, Prof. O. J. Lodge, D. MacAlister, Rev. G. Richardson. W. M. Hicks, Prof. O. J. Lodge, D. ilacAlister, Prof. R. C. Rowe. C. Carpmael, W. M. Hicks, Prof. A. Johnson, Prof. O. J. Lodge, Dr. D. MncAlister. R. E. Baynes, R. T. Glazebroob, Prof. W. M. Hicks, Prof. W. Ingram. TBESIDENTS AND SECRETAEIES OF THE SECTIONS. xlv CHEMICAL SCIENCE. COMMITTEE OF SCIENCES, II. — CHEMTSTRT, MINERALOGY. Date and Place Presidents 1832. 18.33. 1834. 183.5. 1836. 1837. 1838. 1839. 1840. Oxford Cambridge Edinburuh ■John Dalton, D.C.L., F.R.S. ; John Dalton, D.C.L., F.R.S. Dr. Hope Secretaries James F. W. Johnston. Prof. Miller. Mr. Johnston, Dr Christison. Dublin . Bristol . Liverpool... Newcastle Birmingham Glasgow ... 1841. Plymouth... 1842. 1843. 1844. 1845. 1846, 1847. 1848. 1849. 1850. 1851. 1852. Manchester Cork York Cambridge Soiithamp- ton Oxford SECTION B, — CHEMISTRY AND MINERALOGY. Dr. T. Thomson, F.R.S IDr. Apjohn, Prof. Johnston. Rev. Prof. Gumming Dr. Apjohn, Dr. C.Henry, \V. Hera- path. Prof. Johnston, Prof. Miller, Dr. Reynolds. Prof. Miller, H. L. Pattinson, Thomas Richardson. Dr. Golding Bird, Dr. J. B. Melson. Dr. R. D/Thomson, Dr. T. Clark, Dr. L. Playfair. J. Prideaux, Robert Hunt, W. M. Tweedy. Dr. L. Playfair, R. Hunt, J. Graham. R. Hunt, Dr. Sweeny. Dr. I.. Playfair, E. Solly, T. H. Barker. R. Hunt, J. P. Joule, Prof. Miller, E. Solly. Dr. Miller, R. Hunt, W. Randall. Swansea ... Birmingham Edinburgh Ipswich . . . Belfast 1853. Hull 1854. 1855. 1856. 1857. 1858. 1859. 1860. 1861, 1862. Liverpool Glasgow .,. Cheltenham Dublin Leeds Aberdeen... Oxford Manchester Cambridge 1863. Newcastle 1864. 1865. Bath Birmingham Michael Faraday, F.R.S Rev. William Whewell,F.R.S. Prof. T. Graham, F.R.S Dr. Thomas Thomson, F.R.S. Dr. Daubeny, F.R.S John Dalton, D.C.L., F.R.S. Prof. Apjohn, M.R.LA Prof. T. Graham, F.R.S Rev. Prof. Gumming Michael Faraday, D.C.L., F.R.S. Rev. W. V. Harcourt, M.A., F.R.S. Richard Phillips, F.R.S John Perc3% M.D., F.R.S Dr. Christison, V.P.R.S.B. Prof. Thomas Graham, F.R.S. Thomas Andrews,M.D., F.R.S. Prof. J. F. W. Johnston, M.A., F.R.S. Prof.W. A.Miller, M.D.,F.R.S. Dr. Lyon Playfair.C.B., F.R.S. Prof. B. C. Brodie, F.R.S. ... Prof. Apjohn, M.D., F.R.S., M.R.LA. Sir J. F. W. Herschel, Bart., D.C.L. Dr. Lyon Playfair, C.B., F.R.S. Prof.B. C. Brodie, F.R.S Prof. W.A.Miller, M.D.,F.R.S. Prof. W.A.Miller, M.D.,F.R.S. Dr. Alex. W. Williamson, F.R.S. W.Odling, M.B.,F.R.S.,F.C.S. Prof. W. A. Miller, M.D., Y.P.R.S. B. G. Brodie, R. Hunt, Prof. Solly. T. H. Henry, R. Hunt, T. AVilliams. R. Hunt, G. Shaw. Dr. Anderson, R. Hunt, Dr. Wilson. T. J. Pearsall, W. S. Ward. Dr. Gladstone, Prof. Hodges, Prof. Ronalds. H. S. Blimdell, Prof. R. Hunt, T. J. Pearsall. Dr.Ed wards, Dr. Gladstone, Dr.Price. Prof. Frankland, D)-. H. E. Roscoe. J. Horsley, P. J. Worsley, Prof. Voelcker. Dr. Davy, Dr. Gladstone, Prof. Sul- livan. Dr. Gladstone, W. Odling, R. Rey- nolds. J. S. Brazier, Dr. Gladstone, G. D. Liveing, Dr. Odling. A. Vernon Harcourt, G. D. Liveing, A. B. Northcote. A. Vernon Harcourt, G. D. Liveinc. H. W. Elphinstone, W. Odling, Prof. Roscoe. Prof. Liveing, H. L. Pattinson, J. C. Stevenson. A.V.Harcourt,Prof.Liveing,R.Biggs. A. V. Harcourt, H. Adkiris, Prol. Wanklyn, A. Winkler Wills. xlvi EEPOKT 1885. Date and Place 1866. Nottingham 1867. Dundee ... 1868. Norwich ... 1869. Exeter 1870. Liverpool... 1871. Edinburgh 1872. Brighton.. 1873. Bradford.. 1874. Belfast 1875. Bristol 1876. Glasgow .. 1877. Plymouth.. 1878. Dublin 1879. Sbeffield .. 1880. Swansea .. Presidents Secretaries H. Bence Jones, M.D.,F.E.S. 1881. York. 1882. Southamp ton Prof. H. E. Roscoe, B.A., F.R.S., F.C.S. Prof. T. Andrews, M.D.,F.R.S. J. H. Atherton, Prof. Liveing, W. J. Russell, J. White. Prof. T. Anderson, M.D., A. Crum Brown, Prof. G. D. Liveing, F.R.S.E. i W. J. Russell. Prof. E. Frankland, F.R.S., Dr. A. Crum Brown, Dr. W. J. Rus- F.C.S. sell, F. Sutton. Dr. H. Debus, F.R.S., F.C.S. Prof. A. Crum Brown, Dr. W. J. Russell, Dr. Atkinson. Prof. A. Crum Brown. A. E. Fletcher, Dr. W. J. Russell. J. T. Buchanan, W. N. Hartley, T. E. Thorpe. Dr. J. H. Gladstone, F.R.S.... Dr. Mills, W. Chandler Roberts, Dr. ! W. J. Russell, Dr. T. Wood. Prof. W. J. Russell, F.R.S.... , Dr. Armstrong, Dr. Mills, W. Chand- J ler Roberts, Dr. Thorpe. Prof. A. Crum Brown, M.D., Dr. T. Cranstoun Charles, W. Chand- F.R.S.E., F.C.S. I ler Roberts, Prof. Thorpe. A. G. Vernon Harcourt, M.A., Dr. H. E. Armstrong, W. Chandler F.R.S., F.C.S. 1 Roberts, W. A. Tilden. W. H. Perkin, F.R.S W. Dittmar, W. Chandler Roberts, J. M. Thomson, W. A. Tilden. F. A. Abel, F.R.S., F.C.S. ... Dr. Oxland. W. Cliandler Roberts, I J. M. Thomson. Prof. Maxwell Simpson, M.D.,'W. Chandler Roberts, J. M. Thom- F.R.S., F.C.S. I son. Dr. C. R. Tichborne, T. Wills. Prof. Dewar, M.A., F.R.S. IH. S. Bell, W. Chandler Roberts, J. M. Thomson. Joseph Henry Gilbert, Ph.D.,' H. B. Dixon, Dr. W. R. Eaton Hodg- F.R.S. kinson, P. Phillips Bedson, J. M. Thomson. Prof. A. W.Williamson, Ph.D., P. Phillips Bedson, H. B. Dixon, F.R.S. 1 T. Gough. Prof. G. D. Liveing, M.A., P. Phillips Bedson, H. B. Dixon, F.R.S. I J. L. Notter. 1883. Southport Dr. J. H. Gladstone, F.R.S... I Prof. P. Phillips Bedson, H. B. ' ! Dixon, H. Forster Morley. 1884. Montreal ... Prof. Sir H. E. Roscoe, Ph.D., Prof. P. Phillips Bedson, H.B. Dixon, LL.D., F.R.S. T. McFarlane, Prof. W. H. I'ikc. 188.'5. Aberdeen... Prof. H. E. Armstrong, Ph.D., Prof. P.Phillips Bedson, H. B. Dixon, I F.R.S., Sec. C.S. : H. Forster Morley, Dr. W. J. I I Simpson. GEOLOGICAL (and, until 1851, GEOGRAPHICAL) SCIENCE. COMMITTEE OF SCIENCES, III. — GEOLOGY AND GEOGKAPHY. 1832. Oxford IR. L Murchi.sou, F.R.S ^ John Taylor. 1833. Cambridge. !g. B. Greenough, F.R.S W. Lonsdale, John Phillips. 1834. Edinburgh .[Prof. Jameson ! Prof . Phillips, T. Jameson Torrie, i Rev. J. Yates. 1835. Dublin. 1836. Bristol . 1837. Liverpool... SECTION C. — GEOLOGY AND GEOGKAPHY. R. J. Griffith ; Captain Portlock, T. J. Torrie. Rev. Dr. Buckland, F.R.S. — William Sanders, S. Stutchbury, 6^e(>(/>'ff/^7i!y, R. L Murchison, ! T.J. Torrie. F.R.S. j Rev. Prof. Sedgwick, F.R.S.— ; Captain Portlock, R. Hunter. — Geo- Geoffrap7iy,G.'B.GYeenough, fjraphy, Captain H. M. Denham, F.R.S. R.N. PRESIDENTS AND SECRETARIES OF THE SECTIONS. xlvii Date and Place 1838. Newcastle. . 1839. Birmingham 1S40. Glasgow ... 1811. Plymouth... 1842. Manchester 1843. Cork 1844. York 1845. Cambridge. 1846. Southamp- ton. 1847. Oxford 1848. Swansea ... 1 849.Birmingham 1850. Edinburgh' Presidents C. Lyell, F.K.S., V.P.G.S.— Geoqraphy, Lord Prudhope. Kev. i)r. Buckland, F.R.S.— Gcoqraphy, G.B.Greenough, F.R.S. Charles Lyell, F.R.S.— C'ert- graj>hy, G. B. Greenough, F.R.S. H. T. Dela Beche, F.R.S. ... R. I. Mm-chison, F.R.S Richard E. Griffith, F.R.S., M.R.LA. Henry Warbui-ton, M.P.,Pres. Geol. Soc. Rev. Prof. Sedgwick, M.A., F.R.S. Leonard Horner,F.R.S. — Geo- graphy, G. B. Greenough, F.R.S. Very Rev.Dr.Buckland,F.R.S. Sir H. T. De la Beche, C.B., F.R.S. Sir Charles Lyell, F.R.S., F.G.S. Sir Roderick I. Murchison, F.R.S. Secretaries W. C. Trevelyan, Capt. Portlock. — Geoqraphy, Capt. Washington. George Lloyd, M.D., H. E. Strick- land, Charles Darwin. W. J. Hamilton, D. Milne, Hugh Murray, H. E. Strickland, John Scoular, M.D. W. J. Hamilton, Edward Moore, M.D., R. Hutton. E. W. Binney, R. Hutton, Dr. R. Lloyd, H. E. Strickland. Francis M. Jennings, H. E. Strick- land. Prof. Ansted, E. H. Bunbury. Rev. J. C. Gumming, A. C. Ramsay, Rev. W. Thorp. Robert A. Austen, Dr. J. H. Norton, Prof. Oldham. — Geoyrajjhy, Dr. C. T. Beke. Prof. Ansted, Prof. Oldham, A. C. Ramsay, J. Ruskin. Starling Benson, Prof. Oldham, Prof. Ramsay. J. Beete Jukes, Prof. Oldham, Prof. A. C. Ramsay. A. Keith Johnston, Hugh Miller, Prof. Nicol. 1851. Ipswich 1852. Belfast. 1853. Hull 1854. Liverpool . . 1855. Glasgow ... 1856. Cheltenham 1857. Dublin 1858. Leeds 1859. Aberdeen... 1860. Oxford 1861. Manchester 1862. Cambridge SECTION c (^continued'). — geology. WilliamHopkins, M. A.,F.R.S. Lieut-Col. Portlock, R.E., F.R.S. Prof. Sedgwick, F.R.S Prof. Edward Forbes, F.R.S. Prof. A. C. Ramsay, F.R.S.... The Lord Talbot de Malahide C. J. F. Bunbuiy, G. W. Ormerod, Searles Wood. James Bryce, James MacAdam, Prof. M'Coy, Prof. Nicol. Prof. Harkness, William Lawton. John Cunningham, Prof. Harkness, G. W. Ormerod, J. W. Woodall. Sir R. I. Murchison, F.R.S.... James Bryce, Prof. Harkness, Prof. Nicol. Rev. P. B. Brodie, Rev. R. Hep- worth, Edward Hull, J. Scougall, T. Wright. Prof. Harkness, Gilbert Sanders, Robert H. Scott. William Hopkins,M.A.,LL.D., Prof. Nicol, H. C. Sorby, E. W. F.R.S. Shaw. Sir Charles Lyell, LL.D., Prof. Harkness, Rev. J. Longmuir, D.C.L., F.R.S. j H. C. Sorby. Rev. Prof. Sedgwick, LL.D.,! Prof. Harkness, Edward Hull, Capt. F.R.S., F.G.S. D. C. L. Woodall. Sir R. I. Murchison, D.C.L., Prof. Harkness, Edward Hull, T. LL.D., F.R.S. Rupert Jones, G. W. Ormerod. J. Beete Jukes, M.A., F.R.S. Lucas Barrett, Prof. T. Rupert Jones, H. C. Sorby. ' At a meeting of the General Committee held in 1850, it was resolved ' That the subject of Geography be separated from Geology and combined with Ethnology, to constitute a separate Section, under the title of the " Geographical and Ethno- logical Section," ' for Presidents and Secretaries of which see page lii. xlviii EEPORT — 1885. Date and Place 1863. Newcastle 1864. Bath 1865. Birminghani 1866. Nottingham 1867. Dundee ... 1868. Norwich ... 1869. Exeter 1870. Liverpool... 1871. Edinburgh 1872. Brighton... 187.3. Bradford... 1874. Belfast 1875. Bristol 1876. Glasgow .. 1877. Plymouth... 1878. Dublin 1879. Sheffield ... 1880. Swansea ... 1881. York 1882. Southamp- ton. 1883. Southport 1884. Montreal ... 1885. Aberdeen... Presidents Secretaries Prof. Warington W. Smyth, F.R.S., F.G.S, Prof. J. Phillips, LL.D., F.E.S., F.G.S. Sir R. I. MurchisoD, Bart., K.C.B. Prof. A. C. Ramsay. LL.D., F.R.S. Archibald Geikie, F.R.S., F.G.S. R. A. C. Godwin-Austen, F.R.S., F.G.S. Prof. R. Harkness, F.R.S., F.G.S. SirPhilipde M.Grey Es^erton, Bart., M.P., F.R.S. Prof. A. Geikie, F.R.S., F.G.S. R. A. C. Godwin-Austen,] F.R.S., F.G.S. Prof. J. Phillips, D.C.L., F.R.S., F.G.S. Prof. Hull, M.A., F.R.S., F.G.S. Dr. Thomas Wright, F.R.S.E., F.G.S. Prof. John Yoiing, M.D W. Pengelly, F.R.S .John Evans, D.C.L., F.R.S., F.S.A., F.G.S. Prof. P. Martin Duncan, M.B., F.R.S., F.G.S. H. C. Sorby, LL.D., F.R.S., F.G.S. A. C. Ramsay, LL.D., F.R.S., V c ^ R. Etheridge, F.R.S., F.G.S. Prof. W. C. Williamson, LL.D., F.R.S. W. T. Blanford, F.R S., Sec. G.S. Prof. .7. W. Judd, F.R.S., Sec. G.S. E. F. Boyd, John Daglish, H. C. Sorbv, Thomas Sopwith. W. B. Dawkins, J. Johnston, H. C. Sorbj', W. Pengelly. Rev. P. B. Brodie, J. Jones, Rev. E. Myers, H. C. Sorby, W. Pengelly. R. Etheridge, W. Pengelly, T. Wil- son, G. H. Wright. Edward Hull, W. Pengelly, Henry Woodward. Rev. 0. Fisher, Rev. J, Gunn, W. Pengelly, Eov. H. H. Wiuwood. W. Pengelly, W. Boyd Dawkins. Rev. n. H. Winwood. W. Pengelly, Rev. H. H. Winwood, W. Boyd Dawkins, G. H. Morton. R. Etheridge, J. Geikie, T. McKennv Hughes, L. C. Miall. L. C. Miall, George Scott, William Topley, Henry Woodward. L. C. Miall, R. H. Tiddeman, W. Topley. F. Drew, L. C. Jliall, R. G. Symes, R. H. Tiddeman. L. C. Miall, E. B. Tawney, W. Top- ley. J. Armstrong, F. W. Rudler, W. Topley. Dr. Le Neve Foster, R. H. Tidde- man, W. Topic)'. E. T. Hardman, Prof. J. O'Reill}-, R. H. Tiddeman. W. Topley, G. Blake Walker. W. Topley, W. Whitaker. J. E. Clark, W. Keeping, W. Topley, W. Whitaker. T. AV. Shore, W. Topley, E. West- lake, W. Whitaker. R. Betley, C. E. De Ranee, W. Top- ley, W. Whitaker. F. Adams, Prof. E. W. Claypole, W. Topley, W. Whitaker. C. E. De Ranee. J. Horne, J. J. H. 1 Teall, W. Topley. BIOLOGICAL SCIENCES. COMMITTEE Of SCIENCES, IV. — ZOOLOGY, BOTANY, PHYSIOLOGY, ANATOMY. 1832. Oxford lEev. P. B. Duncan, F.G.S. ...IRev. Prof. J. S. Henslow. 1833. Cambridge' Rev. W. L. P. Garnons, F.L.S. ' C. C. Babinglon, D. Don. 1834. Edinburgh. Prof. Graham |W. Yarrell, Prof. Burnett. ' At this Meeting Physiology and Anatomy were made a separate Committee, for Presidents and Secretaries of which see p. li. PRESIDENTS AND SECBETAEIES OF THE SECTIONS. SECTION D. — ZOOLOGT AND BOTANY. xlix Date and Place Presidents 1835. Dublin. 1836. Bristol. Dr. Allman Rev. Prof. Henslow 1837. Liverpool... 1838. Newcastle 1 839. Birmingham 1840. Glasgow ... 1841. Plymouth... 1842. Manchester W. S. MacLeay Sir W. Jardine, Bart. Prof. Owen, F.R.S Sir W. J. Hooker, LL.D. 1843. Cork. 1844. York. 1845. Cambridge 1846. Southamp- ton. 1847. Oxford John Richardson, M.D., F.R.S. Hon. and Very Rev. W. Her- bert, LL.D., F.L.S. William Tliompson, F.L.S. ... Very Rev. the Dean of Man- chester. 'Rev. Prof. Henslow, F.L.S.... I Sir J. Richardson, M.D., j T? T? S H. E. Strickland, M.A., F.R.S. Secretaries J. Curtis, Dr. Litton. J. Curtis, Prof. Don, Dr. Riley, S. Eootsey. C. C. Babington, Rev. L. Jenyns, W. Swainson. J. E. Gray, Prof. Jones, R. Owen, Dr. Richardson. E. Forbes, W. Ick, R. Patterson. Prof. W. Couper, E. Forbes, R. Pat- terson. J. Couch, Dr. Lankester, R. Patterson. Dr. Lankester, E. Patterson, J. A. Turner. G. J. Allman, Dr. Lankester, R. Patterson. Prof. Allman, H. Goodsir, Dr. King, Dr. Lankester. Dr. Lankester, T. V. Wollaston, Dr. Lankester, T. V. Wollaston, H. Wooldridge. Dr. Lankester, Dr. Melville, T. V. Wollaston. 1849. Birmingham 1850. Edinburgh 1851. Ipswich ... 1852. Belfast 1853. Hull 1854. Liverpool... 1855. Glasgow ... 1856. Cheltenham 1857. Dublin 1858. Leeds 1859. Aberdeen... 1860. Oxford 1861. Manchester 1862. Cambridge 1863. Newcastle 1864. Bath 1865. Birmingham 1885. William Spence, F.R.S Prof. Goodsir, F.R.S. L. & E. Rev. Prof. Henslow, M.A., F.R.S. W. Ogilby SECTION D (contimied). — zooLoor and botany, including physiology. [For the Presidents and Secretaries of the Anatomical and Physiological Subsec- tions and the temporary Section E of Anatomy and Medicine, see p. li.] 1848. Swansea ... L. W. Dillwyn, F.R.S Dr. R. Wilbraham Falconer, A. Hen- frey. Dr. Lankester. Dr. Lankester, Dr. Russell. Prof. J. H. Bennett, M.D., Dr. Lan- kester, Dr. Douglas Maclagan. Prof. Allman, F. W. Johnston, Dr. E. Lankester. Dr. Dickie, George C. Hyndman, Dr. Edwin Lankester. Robert Harrison, Dr. E. Lankester. Isaac Byerley, Dr. E. Lankester. William Keddie, Dr. Lankester. Dr. J. Abercrombie, Prof. Buckman, Dr. Lankester. Pro^:. J. R. Kinahan, Dr. E. Lankester, Robert Patterson, Dr. W. E. Steele. Henry Denny, Dr. Heaton, Dr. E. Lankester, Dr. E. Perceval Wright. Prof. Dickie, M.D., Dr. E. Lankester, Dr. Ogilvy. W. S. Church, Dr. E. Lankester, P, L. Sclater, Dr. E. Perceval Wright. Dr. T. Alcock, Dr. E. Lankester, Dr. P. L. Sclater, Dr. E. P. Wright. Alfred Newton, Dr. E. P. Wright. Dr. E. Charlton, A. Newton, Rev. H. B. Tristram, Dr. E. P. Wright. H. B. Brady, C. E. Broom," H. T. Stainton, Dr. E. P. Wright. Dr. J. Anthony, Rev. C. Clarke, Rev. H. B. Tristram, Dr. E. P. Wright. c C. C. Babington, M.A., F.R.S. Prof. Balfour, M.D., F.R.S.... Rev. Dr. Fleeming, F.R.S.E. Thomas Bell, F.R.S., Pres.L.S. Prof. W. H. Harvey, M.D., F.R.S. C. C. Babington, M.A., F.R.S. Sir W. Jardine, Bart., F.R.S.E. Rev. Prof. Henslow, F.L.S.... Prof. C. C. Babington, F.R.S. Prof . Huxley, F.R.S Prof. Balfour, M.D., F.R.S.... Dr. John E. Gray, F.R.S. ... T. Thomson, M.D., F.R.S. ... REPORT — 1885. SECTION D {continued). — biologt.' Date and Place 1866. Nottingham 1867. Dundee 1868. Norwich 1869. Exeter. 1870. Liverpool. 1871. Edinburgh 1872. Brighton 1873. Bradford 1874, Belfast . 1875. Bristol 1876. Glasgow 1877. Plymouth.. Presidents Prof. Hiixley, LL.D., F.R.S. — Pliijsiulo/i'ical Dcj>., Prof. Humphry," M.D., F.R.S.— Aiithropohf/ieal I)vp., Alf. K. Wallace, F.R.G.S. Prof. Sharpey, M.D., Sec. R.S. — Bcj). of Zool. and Bat., George Busk, M.D., F.K.8. Rev. M. J. Berkeley, F.L.S. — Dvp. of Physiohfiy, W. H. Flower, F.R.S. George P.usk, F.R.S., F.L.S. — -Dcp. of Hot. and Zool., C. Spence Bate, F.R.S. - Dc2>. of Ethno., E. B. Tylor. Prof.G. iRolle.ston,M.A., M.D., F.R.S., Y.l^.'S. — Bcj). of Aiiat. and P/ii/mil.,FTot.M. P'oster, M.D., F.L.S.— i>(y. of Ethno., J. Evans, F.R.S. Prof. Allen Thomson, M.D., ¥.IX.^.—Dep. of Bot. and .^w*^.,rrof.WyvilleThomson, F.R.S.— Z'cy;. of Antfirojwl., Prof. W. Turner, M.D. Sir J. Lubbock, Bart., F.R.S.— Bej). of Anut. and Physiol., Dr. Burdon Sanderson, F.R.S.— Z)<y». ofAnthrojwl, Col. A. Lane Fox, F.G.S. Prof. Allman, F.R.S.— Brj>. of A nat.and Physiol. ,Vr:oi. Ru- therford, M.D. — Bvp-ofAn- thropol.. Dr. Beddoe, F.R.S. Prof. Redfern, M..V).—B(p. of Zool. and Bot., Dr. Hooker, C.B.,Pres.R.S.— i>(7Ao/^«- throp., Sir W.R.Wilde, M.D. P. L. Sclater, F.R.S.— Z**-^. o/ .1 nat.and Ph ifsiol.,Vr:oi.C\Q land, M.D., V.H.'&.—Bep.of Anthropol., Prof. Rolleston, M.D., F.R.S. A. Russel Wallace, F.R.G.S., F.L.S.— i?(y. of Zool. and Bot., Prof. A. Newton, M.A., ¥.B,.S.—Bep. of Anat. and Phi/siol, Dr. J. G. McKen- drick, P.R.S.E. .J.awynJeffreys,LL.D.,F.R.S., F.L.S. — Bep. of Anat. and Phy.noL, Prof. Macalister, Secretaries Dr. J. Beddard, W. Felkin, Rev. H. B. Tristram, W. Turner, E. B. Tylor, Dr. E. P. Wright. C. Spence Bate, Dr. S. Cobbold, Dr. U. Foster, H. T. Stainton, Rev. H. B. Tristram, Prof. W. Turner. Dr. T. S. Cobbold, G. W. Firth, Dr. M. Foster, Prof. Lawson, H. T. Stainton, Rev. Dr. H. B. Tristram, Dr. E. P. Wrisrht. Dr. T. S. Cobbold, Prof. M. Foster, E. Ray Lankester, Prof. Lawson, H. T Stainton, Rev. H. B. Tris- tram. Dr. T. S. Cobbold, Sebastian Evans, Prof. Lawson, Thos. J. Moore, H. T. Stainton, Rev. H. B. Tri.stram, C. Staniland Wake, E. Ray Lan- kester. Dr. T. R. Eraser, Dr. Arthur Gamgee, E. Ray Lankester, Prof. Lawson, H. T. Stainton, C. Staniland Wake, Dr. W. Rutherford, Dr. Kelburne King. Prof. Thiselton-Dyer, H. T. Stainton, Prof. Lawson, F. W. Rudler, J. H. Lamprey, Dr. Gamgee, E. Ray Lankester, Dr. Pye-Smith. Prof. Thiselton-Dyer, Prof. Lawson, R. JI'Lachlan, Dr. Pye-Smith, E. Ray Lankester, F. W. Rudler, J. H. Lamprey. W.T. Thiselton- Dyer, R. O. Cunning- ham, Dr. J. J. Charles, Dr. P. H. Pye-Smith, J. J. Murphy, F. W. Rudler. E. R. Alston, Dr. McKendrick, Prof. W. R. M'Nab, Dr. Martyn, F. W. Rudler, Dr. P. H. Pye-Smith, Dr. W. Spencer. E. R. Alston, Hvde Clarke, Dr Knox, Prof. W." R. M'Nab, Dr. Muirhead, Prof. Morrison Wat- son. E. R. Alston, F. Brent, Dr. D. J Cunningham, Dr. C. A. Hingston, Prof. W. R. M'Nab, J. B. Rowe, F. W. Rudler. M.D.~Bep. of Anthropol., Francis Galton, M.A.,F.R.S. ' At a meeting of the General Committee in 1865, it was resolved : — ' That the title of Section D be changed to Biology ; ' and ' That for the word " Subsection," in the rules for conducting thebusiness of the Sections, the word "Department" be substituted.' PRESIDENTS AND SECRETARIES OF THE SECTIONS. li Date and Place 1878. Dublin , 1879. Sheffield ... 1880. Swansea 1881. York. 1882. Southamp- ton. 1883. Southport' 1884. Montreal-... 1885. Aberdeen... 'Presidents Prof. W. H. Flower, F.R.S.— Bcp. of AnthrojMl., Prof. Huxley, Sec. R.S. — Bip. of A/iat. and Physiol., R. McDonnell, M.D., F.R.S. Prof. St. George Mivart, F.R.S.— Z)e/A 4 Anthropol., E. B. Tylor, D.C.L., F.R.S. — Bep. of Anat. and Phi/- mil.. Dr. Pye-Smith. A. C. L. Giinther, M.D., F.R.S. — Dcp. of Anat. and Phy- siol, F. M. Balfour, M.A., F.'R.S.—Bep. of Antkropol., F. W. Rudler, F.G.S. Richard Owen, C.B., M.D., F.R.S.^Bep.of AnthropoL, Prof. W. H. Flower, LL.D., F.R.S.— 2)<7A of Anat. and Phymol.,YToi.J. S. Burden Sanderson, M.D., F.R.S. Prof. A. Gamgee, M.D., F.R.S. - Bep. of Zool. and Bot., Prof. M. A. Lawson, M.A., F.Jj.S.— Bep. of Anthropol., Prof. W. Boyd Dawkins, M.A., F.R.S. Prof. E. Ray Lankester, M.A., F.R.S.— D^jy;. of Anthropol., W. Pengelly, F.R.S. Prof. H. N. Moseley, M.A., F.R.S. Prof. W. C. Mcintosh, M.D., LL.D., F.R.S. L. & E. Secretaries Dr. R. J. Harvey, Dr. T. Hayden, Prof. W. R. M'Nab, Prof. J. M. Purser, J. B . Rowe, F. W. Rudler. Arthur Jackson, Prof. W. R. M'Nab, J. B. Rowe, F. W. Rudler, Prof. Schiifer. G. W. Bloxam, John Priestley, Howard Saunders, Adam Sedg- wick. G. W. Bloxam, W. A. Forbes, Rev. W. C. Hey, Prof. W. R. M'Nab, W. North, John Priestley, Howard Saunders, H. E. Spencer. G. W. Bloxam, W. Heape, J. B. Nias, Howard Saunders, A. Sedg- wick, T. W. Shore, jun. G. W. Bloxam, Dr. G. J. Haslam, W. Heape, W. Hurst, Prof. A. M. Marshall, Howard Saunders, Dr. G. A. Woods. Prof. W. Osier, Howard Saunders, A. Sedgwick, Prof. R. R. Wright. W. Heape, J. McGregor- Robertson, J. Duncan Matthews, Howard Saunders, H. Marshall Ward. ANATOMICAL AND PHYSIOLOGICAL SCIENCES. COMMITTEE OF SCIENCES, V. — ANATOMY AND PHYSIOLOGY. 1833. Cambridge |Dr. Haviland iDr. Bond, Mr. Paget. 1834. Edinburgh |Dr. Abercrombie iDr. Roget, Dr. William Thomson. SECTION E (until 1847). — ANATOMY AND MEDICINE. 183.5. Dublin 1836. Bristol 1887. Liverpool... 1838. Newcastle 1839. Birmingham 1840. Glasgow ... 1841. Plymouth... Dr. Pritchard Dr. Roget, F.R.S Prof. W. Clark, M.D. T. E. Headlam, M.D John Yelloly, M.D., F.R.S... James Watson, M.D P. M. Roget, M.D., Sec. R.S. Dr. Harrison, Dr. Hart. Dr. Symonds. Dr. J. Carson, jun., James Long, Dr. J. R. W. Vose. T. M. Greenhow, Dr. J. R. W. Vose. Dr. G. O. Rees, F. Ryland. Dr. J. Brown, Prof. Couper, Prof Reid. Dr. J. Butter, J. Fuge, Dr. R. R Sargent. ' By direction of the General Committee at Southampton (1882) the Departments ■of Zoology and Botany and of Anatomy and Physiology were amalgamated. -By authority of the General Committee, Anthropology was made a separate Section, for Presidents and Secretaries of which see p. Ivii. c2 lii REPORT 1885. SECTION E. PHYSIOLOGY. Date and Place 1842. Manchester 1843. Cork 1844 York 1845. Cambridge 1846. Southamp- ton. 1847. Oxford' ... Presidents Secretaries Edward Holme, M.D., F.L.S.'Dr. Cliaytor, Dr. R. S. Sargent. Sir James Pitcairn, M.D. J. C. Pritchard, M.D Prof. J. Haviland, M.D. . Prof. Owen, M.D., F.R.S. Prof. Ogle, M.D., F.R.S. . Dr. John Popham, Dr. R. S. Sargent. I. Erichsen, Dr. R. S. Sargent. Dr. R. S. Sargent, Dr. Webster. C. P. Keele, Dr. Laycock, Dr. Sar- gent. Dr. Thomas K. Chambers, W. P. Ormerod. 1850. 1855. 1857. 1858, 1859. 1860. 1861. 1862. 1863. 1864. 1865. Edinburgh Glasgow ... Dublin Leeds Aberdeen... Oxford Manchester Cambridge Newcastle Bath Birming- ham.^ PHYSIOLOGICAL SUBSECTIONS OF SECTION D. Prof. Bennett, M.D., F.R.S.E. Prof. Allen Tliomson, F.R.S. Prof. R. Harrison, M.D Sir Benjamin Brodie, Bart., F.R.S. Prof. Sliarpev, M.D., Sec.R.S. Prof. G. RoUeston, M.D., F.L.S. Dr. John Davy, F.R.S.L.& E. G. E. Paget, M.D Prof. Rolleston, M.D., F.R.S. Dr. Edward Smith, LL.D., F.R.S. Prof. Acland, M.D., LL.D., F.R.S. Prof. J. H. Corbett, Dr. J. Struthers. Dr. R. D. Lyons, Prof. Redfern. C. G. Wheelhouse. Prof. Bennett, Prof. Redfern. Dr. R. M'Donnell, Dr. Edward Smith. Dr. W. Roberts, Dr. Edward Smith. G. F. Helm, Dr. Edward Smith. Dr. D. Embleton, Dr. W. Turner. J. S. Bartrum, Dr. W. Turner. Dr. A. Fleming, Dr. P. Hesiop, Oliver Pembleton, Dr. W. Turner. GEOGRAPHICAL AND ETHNOLOGICAL SCIENCES. [For Presidents and Secretaries for Geography previous to 1851, see Section C, , p. xlvi.] ETHNOLOGICAL SUBSECTIONS OF SECTION D. 1846. Southampton 1847. Oxford 1848. Swansea ... 1849. Birmingham 1850. Edinburgh Dr. Pritcliard Dr. King. Prof. H. H. Wilson, M.A. Prof. Buckley. G. Grant Francis. Dr. R. G. Latham. Daniel Wilson. Vice-Admiral Sir A. Malcolm SECTION E. — GEOGRAPHY AND ETHNOLOGY. R. Cull, Rev. J. W. Donaldson, Dr. Norton Shaw. R. Cull, R. MacAdam, Dr. Norton Shaw. R. Cull, Rev. H. W. Kemp, Dr. Norton Shaw. Richard Cull, Rev. H. Higgins, Dr. Hine, Dr. Norton Shaw. Dr. W. G. Blackie, R. Cull, Dr. Norton Shaw. R. Cull, F. D. Hartland, W. H. Rumsey, Dr. Norton Shaw. R. Cull, S. Ferguson, Dr. R. R. Madden, Dr. Norton Shaw. ' By direction of the General Committee at Oxford, Sections D and E were incorporated under tlic name of ' Section D — Zoology and Botany, including Phy- siology ' (see p. xlix). The Section lieing then vacant was assigned in 1851 to Geography. * Vide note on page 1. 1851. Ipswich ... 1852. Belfast 1853. Hull 1854. Livei-pool... 18.55. Glasgow ... 1856. Cheltenham 1857. Dublin Sir R. I. Murchison, F.R.S., Pres. R.G.S. Col. Chesney, R.A., D.C.L., F.R.S. R. G. Latham, M.D., F.R.S. Sir R. I. Murchison, D.C.L., F.R.S. Sir J. Richardson, M.D., F.R.S. Col. Sir H. C. Rawlinson, K.C.B. Rev. Dr. J. Henthorn Todd, Pres. R.I.A. PRESIDENTS AND SECRETARIES OF THE SECTIONS. liii Date and Place 1858. Leeds 1859. Aberdeen... 1860. Oxford 1861. Manchester 1862. Cambridge 1863. Newcastle 1864. Bath 1865. Birmingham 1866. Nottingham 1867. Dundee ... 1868. Norwich ... Presidents Sir R.I. Mm-chison,G.C.St.S., F.R.S. Rear - Admiral Sir James Clerk Ross, D.C.L., F.R.S. Sir R. I. Murchison, D.C.L.. F.R.S. John Crawfvird, F.R.S Francis Galton, F.R.S Sir R. I. Murchison, K.C.B., F.R.S. Sir R. I. Murchison, K.C.B., F.R.S. Major-General Sir H. Raw- linson, M.P., K.C.B., F.R.S. Sir Charles Nicholson, Bart.. LL.D. Sir Samuel Baker, F.R.G.S. Capt. G. H. Richards, R.X. F.R.S. Secretaries R. Cull, Francis Galton, P. O'Cal- laghan. Dr. Norton Shaw, Thomas Wright. Richard Cull, Prof.Geddes, Dr. Nor- ton Shaw. Capt. Burrows, Dr. J. Himt, Dr. C. Lempri^re, Dr. Norton Shaw. Dr. J. Hunt, J. Kingsley, Dr. Nor- ton Shaw, W. Spottiswoode. J. W. Clarke, Rev. J. Glover, Dr. Hunt, Dr. Norton Shaw, T. Wright. C. Carter Blake, Hume Greenfield, C. R. Markham, R. S. Watson. H. W. Bates, C. R. Markham, Capt, R. M. Murchison, T. Wright. H. W. Bates, S. Evans, G. Jabet, C. R. Markham, Thomas Wright. H. W. Bates, Rev. E. T. Cusins, R. H. Major, Clements R. JIarkham, D. W. Nash, T. Wright. H. W. Bates, Cyril Graham, Clements R. Markham, S. J. Mackie, R. Sturrock. T. Baines, H. W. Bates, Clements R. Markham, T. Wright. 1869. Exeter 1870. Liverpool.. 1871. Edinburgh 1872. Brighton.. 1873. Bradford.. 1874. Belfast 1875. Bristol 1876. Glasgow .. 1877. Plymouth.. 1878. Dublin 1879. Sheffield .. 1880. Swansea .. 1881. York 1882. Southamp- ton. SECTION E {continued). - Sir Bartle Frere, K.C.B., LL.D., F.R.G.S. Sir R. I.Murcbison,Bt.,K.C.B., LL.D., D.C.L., F.R.S., F.G.S. Colonel Yule, C.B., F.R.G.S. Francis Galton, F.R.S Sir Rutherford Alcock, K. C.B. Major Wilson, R.E., F.R.S., F.R.G.S. Lieut. - General Strachey, R.E.,C.S.I.,F.R.S.,F.R.G.S., F.L.S., F.G.S. Capt. Evans, C.B., F.R.S Adm.SirE. Ommanney, C.B., F.R.S., F.R.G.S., F.R.A.S. Prof. Sir C. Wyville Thom- son, LL.D., F.R.S.L.&E. Clements R. Markham, C.B., F.R.S., Sec. R.G.S. Lieut.-Gen. Sir J. H. Lefroy, C.B., K.C.M.G., R.A., F.R.S., Th' T? P S Sir J. b.' Hooker, K.C.S.L, C.B., F.R.S. Sir R. Temple, Bart., G.C.S.I., F.R.G.S. -GEOGRAPHY. H. W. Bates, Clements R. Markham, J. H. Thomas. H.W.Bates, David Buxton, Albert J. Mott, Clements R. Markham. Clements R. Markham, A. Buchan, J. H. Thomas, A. Keith Johnston. H. W. Bates, A. Keith Johnston, Rev. J. Newton, J. H. Thomas. H. W. Bates, A. Keith Johnston, Clements R. Markham. E. G. Ravenstein, E. C. Rye, J. H. Thomas. H. W. Bates, E. C. Rye, F. F. Tuckett. H. W. Bates, E. C. Rye, R. Oliphant Wood. H. W. Bates, F. E. Fox, E. C. Rye. John Coles, E. C. Rye. H. W. Bates, C. B. D. Black, E. C. Rye. H. W. Bates, E. C. Rye. J. W. Barry, H. W. Bates. E. G. Ravenstein, E. C. Eye. liv EEPORT — 1885. Date and Place Presidents Secretaries 1883. Southport 1884. Montreal .. 1885. Aberdeen., Lieut.-Col. H. H. Godwin- I Austen, F.R.S. Gen. Sir J. H. Lefroy, C'.B., K.C.M.G., F.R.S.,Y.P.R.G.S. Gen. J. T. Walker, C.B., R.E., LL.D., F.E.S. John Coles, E. G. Eavenstein, E. C. Rye. Rev. Abbe Laflamme, J. S. O'Halloran, E. G. Ravenstein, J. F. Torrance J. S. Keltie, J. S. O'Halloran, E. G. Ravenstein, Rev. G. A. Smith. 1833. 1834, STATISTICAL SCIENCE. COMMITTEE OF SCIENCES, VI. — STATISTICS. Cambridge! Prof. Babbage, F.R.S i J. E. Drinkwater. Edinburgh I Sir Charles Lemon, Bart | Dr. Cleland, C. Hope Maclean. SECTION F.— STATISTICS. 1835. 1836. 1837. 1838. 1839. 1840. 1841 1842. 1843. 1844. 1845. 1846. 1847. 1848. 1849. 1850. 1851. 1852. 1853. 1854. 1855. Dublin Bristol Liverpool... Newcastle Birmingham Glasgow ... Pljinouth... Manchester Cork York Cambridge Southamp- ton. Oxford Swansea ... Birmingham Edinburgh Ipswich ... Belfast Hull Liverpool... Glasgow ... Charles Babbage, F.R.S Sir Chas. Lemon, Bart., F.R.S. Rt. Hon. Lord Sandon Colonel Sykes, F.R.S Henry Hallam, F.R.S Rt. Hon. Lord Sandon, M.P., F.R.S. Lieut.-Col. Sykes, F.R.S G. W. Wood, M.P., F.L.S. ... Sir C. Lemon, Bart., M.P. ... Lieut. - Col. Sykes, F.R.S., F.L.S. Rt.Hon. the Earl Fitzwilliam G. R. Porter, F.R.S Travers Twiss, D.C.L.. F.R.S, J. H, Vivian, M.P., F.R.S. ... Rt. Hon. Lord Lyttelton Very Rev. Dr. John Lee, V.P.R.S.E. Sir John P. Boileau, Bart. ... His Grace the Archbishop of Dublin. James Heywood, M.P., F.R.S. Thomas Tooke, F.R.S R. Monckton Milnes, M.P. ... W. Greg, Prof. Longfield. Rev. J. E. Bromby, C. B. Fripp,. James Heywood. W. R. Greg, W. Langton, Dr. W. C. Tayler. W. Cargill, J. Heywood, W.R.Wood. F. Clarke, R. W. Rawson, Dr. W. C. Tayler. C. R. Baird, Prof. Ramsay, E. W. Rawson. Rev. Dr. Byrth, Rev. R. Luney, R. W. Rawson. Rev. R. Luney, G. W. Ormerod, Dr. W. C. Tayler. Dr. D. Bullen, Dr. W. Cooke Tayler.. J. Fletcher, J. Heywood, Dr. Lay- cock. J. Fletcher, Dr. W. Cooke Tayler. J. Fletcher, F. G. P. Neison, Dr. W. C. Tayler, Rev. T. L. Shapcott. Rev. W. H. Cox, J. J. Danson, F. G. P. Neison. J. Fletcher, Capt. R. Shortrede. Dr. Finch, Prof. Hancock, F. G. P. Neison. Prof. Hancock, J. Fletcher, Dr. J. Stark. J. Fletcher, Prof. Hancock. Prof. Hancock, Prof. Ingram, James MacAdam, jun. Edward Cheshire, W. Newmarch. B. Cheshire, J. T. Danson, Dr. W. H. Duncan, W. Newmarch. J. A. Campbell, E. Cheshire, W. New- march, Prof. R. H. Walsh. SECTION F (continued). — economic science ani> statistics. 1856. Cheltenham 1857. Dublin Rt. Hon. Lord Stanley, M.P. His Grace the Archbishop of Dublin, M.R.LA. Rev. C. H. Bromby, E. Cheshire, Dr W. N. Hancock, W. Newmarch, W- M. Tartt. Prof. Cairns, Dr. H. D. Hutton, W.. Newmarch. PRESIDENTS AND SECEETAEIES OF THE SECTIONS. iv Date and Place Presidents Secretaries 1858. Leeds 1859. Aberdeen... 1860. Oxford 1861. Manchester 1862. Cambridge 1863. Newcastle . 1864. Bath 1865. Birmingham 1866. Nottingham 1867. Dundee 1868. Norwich.... 1869. Exeter 1870. Liverpool... 1871. Edinburgh 1872. Brighton... 187.3. Bradford ... 1874. Belfast 1875. Bristol 1876. Glasgow ... 1877. Plymouth... 1878. Dublin 1879. Sheffield ... 1880. Swansea ... 1881. York 1882. Southamp- ton. 1883. Southport 1884. Montreal ... 1885. Aberdeen... Edward Baines Col. Sykes, M.P., F.R.S Nassau W. Senior, M.A William Ne^vmarch, F.R.S... . Edwin Chadwick, C.B William Tite, M.P., F.R.S. ... William Farr, M.D., D.C.L., F.R.S. Rt. Hon. Lord Stanley, LL.D., M.P. Prof. J. E. T. Rogers M. E. Grant Duff, M.P Samuel Brown, Pres. Instit. Actuaries. Rt . Hon. Sir Stafford H. North- cote, Bart., C.B., M.P. Prof. W. Stanley Jevons, M.A. Rt. Hon. Lord Neaves Prof. Henry Fawcett, M.P. ... Rt. Hon. W. E. Forster, M.P. Lord O'Hagan James Heywood, M.A., F.R.S., Pres.S.S. Sir George Campbell, K.C.S.L, M.P. Rt. Hon. the Earl Fortescue Prof. J. K. Ingram, LL.D., M.R.LA. G. Shaw Lefevre, M.P., Pres. S.S. G. W. Hastings, M.P Rt. Hon. M. E. Grant-Duff, M.A., F.R.S. Rt. Hon. G. Sclater-Booth, M.P., F.R.S. R. H. Inglis Palgrave, F.R.S. Sir Richard Temple, Bart., G.C.S.L, CLE., F.R.G.S. Prof. H. Sidgwick, LL.D., Litt.D. T. B. Baines, Prof. Cairns, S. Brown, Capt. Fishbourne, Dr. J. Strang. Prof. Cairns, Edmund Macrory, A. M. Smith, Dr. John Strang. Edmund Macrory, W. Newmarch, Rev. Prof. J. E. T. Rogers. David Chadwick, Prof. R. C. Christie, E. Macrory, Rev. Prof. J. E. T. Rogers. H. D. Macleod, Edmund Macrory. T. Doubleday, Edmund Macrory Frederick Purdy, James Potts. E. Macrory, E, T. Payne. F. Purdy. G. J. D. Goodman, G. J. Johnston, E. Macrory. R. Birkin, jun., Prof. Leone Levi, E. Macrory. Prof. Leone Levi, E. Macrory, A. J. Warden. Rev. W. C. Davie, Prof, Leone Levi. Edmund Macrory, Frederick Purdy, Charles T. D. Acland. Chas. R. Dudley Baxter, E. Macrory, J. Miles Moss. J. G. Fitch, James Meikle. J. G. Fitch, Barclay Phillips. J. G. Fitch, Swire Smith. Prof. Donnell, Frank P. Fellows, Hans MacMordie. F. P. Fellows, T. G. P. Hallett, B. Macrory. A. M'Neel Caird, T. G. P. Hallett, Dr. W. Neilson Hancock, Dr. W. Jack. W. F. Collier, P. Hallett, J. T. Pirn, W. J. Hancock, C. Molloy, J. T. Pirn. Prof. Adamson, R. E. Leader, C. Molloy. N. A. Humphreys, C. Molloy. C. Molloy, W. W. Morrell, J. F. Moss. G. Baden- Powell, Prof. H. S. Fox- well, A. Milnes, C. Molloy. Rev. W. Cunningham, Prof. H. S. Foxwell, J. N. Keynes, C. Molloy. Prof. H. S. Foxwell, J. S. McLennan, Prof. J. Watson. Rev. W. Cunningham, Prof. H. S. Foxwell, C. McCombie, J. P. Moss. 1836. Bristol 1837. Liverpool.. 1838. Newcastle MECHANICAL SCIENCE. SECTION G. — MECHANICAL SCIENCE. Davies Gilbert, D.C.L., F.R.S. Rev. Dr. Robinson Charles Babbage, F.R.S T. G. Bunt, G. T. Clark, W. West. Charles Vignoles, Thomas Webster. R. Hawthorn, C. Vignoles, T. Webster. Ivi REPORT 1885. Date and Place 1839. Binningham 1840. Glasgow .... 1841. Plymouth 1842. Manchester 1843. Cork 1844. York 1845. Cambridge 1846. Southamp- ton. 1847. Oxford 1848. Swansea ... 1849. Birmingham 1850. Edinburgh 1851. Ipswich 1852. Belfast 1853. Hull 1854. Liverpool... 1855. Glasgow ... 1856. Cheltenham 1857. Dublin 1858. Leeds 1859. Aberdeen... 1860. Oxford 1861. Manchester 1862. Cambridge 1863. Newcastle 1864. Bath 1865. Birmingham 1866. Nottingham 1867. Dundee 1868. Norwich ... 1869. Exeter 1870. Liverpool... 1871. Edinburgh 1872. Brighton ... 1873. Bradford ... 1874. Belfast Presidents Prof. Willis, F.K.S., and Robt. Stephenson. Sir John Robinson John Taylor, F.R.S Rev. Prof. Willis, F.R.S Prof. J. Macneill, M.R.LA.... John Taylor, F.R.S George Rennie, F.R.S Rev. Prof. Willis, M.A., F.R.S. Rev. Prof .Walker, M.A.,F.R.S. Rev. Prof .Walker, M.A.,F.R.S. Robert Stephenson, M.P., F.R.S. Rev. R. Robinson William Cubitt, F.R.S John Walker, C.E., LL.D., F.R.S. William Fairbairn, C.E., F.R.S. John Scott Russell, F.R.S. ... W. J. JTacquorn Rankine, C.E., F.R.S. George Rennie, F.R.S Rt. Hon. the Earl of Rosse, F.R.S. William Fairbairn, F.R.S. ... Rev. Prof. Willis, M.A., F.R.S. Prof . W. J. Macquorn Rankine, LL.D., F.R.S. J. F. Bateman, C.E., F.R.S.... Wm. Fairbairn, LL.D., F.R.S. Rev. Prof. Willis, M. A., F.R.S. J. Hawkshaw, F.R.S Sir W. G. Armstrong, LL.D., F.R.S. Thomas Hawksley, V.P.Inst. C.E., F.G.S. Prof.W. J. Macquorn Rankine, LL.D., F.R.S. G. P. Bidder, C.E., F.R.G.S. C. W. Siemens, F.R.S Chas. B. Vignoles, C.E., F.R.S. Prof. Fleeming Jenkin, F.R.S. F. J. Bramwell, C.E W. H. Barlow, F.R.S Prof. James Thomson, LL.D. C.E., F.R.S.E. Secretaries W. Carpmael, William Hawkes, T. Webster. J. Scott Russell, J. Thomson, J. Tod, C. Vignoles. Henry Chat field, Thomas Webster. J. F. Bateman, .J. Scott Russell, J, Thomson, Charles Vignoles. James Thomson, Robert Mallet. Charles Vignoles, Thomas Webster. Rev. W. T. Kingsley. William Betts, jun., Charles Manby. J. Glynn, R. A. Le Mesurier. R. A. Le Mesurier, W. P. Struvd. Charles Manby, W. P. Marshall. Dr. Lees, David Stephenson. John Head, Charles Manby. John F. Bateman, C. B Hancock, Cliarles Manby, James Thomson. James Oldliam, J. Thomson, W. Sykes Ward. John Grantham, J. Oldham, J, Thomson. L. Hill, jun., William Ramsay, J. Thomson. C. Atherton, B. Jones, jun., H. M. Jeffery. Prof. Downing, W.T. Doyne, A. Tate, James Thomson, Henry Wright. J. C. Dennis, J. Dixon, H. Wright. R. Abernethj", P. Le Neve Foster, H. Wright. P. Le Neve Foster, Rev. F. Harrison, Henry Wright. P. Le Neve Foster, John Robinson, H. Wright. W. JL Fawcett, P. Le Neve Foster. P. Le Neve Foster, P. Westmacott, J. F. Spencer. P. Le Neve Foster, Robert Pitt. P. Le Neve Foster, Henry Lea, W. P. Marshall, Walter May. P. Le Neve Foster, J. F. Iselin, M. 0. Tarbotton. P. Le Neve Foster, John P. Smith, W. W. Urquliart. P. Le Neve Foster, J. F. Iselin, C. Manby, W. Smith. P. Le Neve Foster, H. Bauerman. H. Bauerman, P. Le Neve Foster, T. King, J. N. Shoolbred. H. Bauerman, Alexander Leslie, J. P. Smith. H. M. Brunei, P. Le Neve Foster, J. G. Gamble, J. N. Shoolbred. Crawford Barlow, H. Bauerman, E. H. Carbutt, J. C. Hawkshaw, J. N. Shoolbred. A. T. Atchison, J. N. Shoolbred, John Smyth, jun. PRESIDENTS AND SECRETARIES OF THE SECTIONS. Ivii Date and Place 1875. Bristol 1876. Glasgow .. 1877. Plj-mouth.. 1878. Dublin 1879. Sheffield .. 1880. Swansea .. 1881. York Presidents Secretaries 1882. Southamp- ton. 1883. Southport 1884. Montreal .. 1885. Aberdeen.. W. Froude, C.E., M.A., F.R.S. C. W. Merrifield, F.R.S Edward Woods, C.E Edward Easton, C.E J. Robinson, Pres. Inst. Mech. Eng. James Abernethy, V.P.Inst. O.E., F.R.S.E. Sir W. G. Armstrong, C.B., LL.D., D.C.L., F.R.S. John Fowler, C.E., F.G.S. ... James Brunlees, F.R.S.E., Pres.Inst.C.E. Sir F. J. Bramwell, F.R.S., V.I'.Inst.C.E. B. Baker, M.Inst.C.E W. R. Browne, H. M. Brimel, J. G. Gamble, J. N. Shoolbred. W. Bottomlev, jun., W. J. Millar, J. N. Shoolbred, J. P. Smith. A. T. Atchison, Dr. Merrifield, J. N. Shoolbred. A. T. Atchison, R. G. Symes, H. T. Wood. A. T. Atchison, Emerson Bainbridge, H. T. Wood. A. T. Atchison, H. T. Wood. A. T. Atchison, J. F. Stephenson, H. T. Wood. A. i'. Atchison, F. Ghurton, H. T. Wood. A. T. Atchison, E. Rigg, H. T. Wood. A. T. Atchison, W. B. Dawson, J. Kennedy, H. T. Wood. A. T. Atchison, F. G. Ogilvie, E. Rigg, J. N. Shoolbred. ANTHROPOLOGICAL SCIENCE. 1884. Montreal.. 1885. Aberdeen.. SECTION H. — ANTHROPOLOGY. E. B. Tylor, D.C.L., F.R.S. ... Francis Galton, MA., F.R.S. G. W. Bloxam, W. Hurst. G. W. Bloxam, Dr. J. G. Garson, W. Hurst, Dr. A. Macgregor. LIST OF EVENING LECTURES. Date and Place 1842. Manchester J1843. Cork 1844. York , 1845. Cambridge 1846. Southamp- ton, 1847. Oxford. Lecturer Charles Vignoles, F.R.S. . Sir M. I. Brunei R. I. Murchison Prof. Owen, M.D., F.R.S... Prof. E. Forbes, F.R.S Dr. Robinson Charles Lyell, F.R.S Dr. Falconer, F.R.S G.B.Airy,F.R.S.,Astron.Royal R. I. Murchison, F.R.S Prof. Owen, M.D., F.R.S. ... Charles Lyell, F.R.S W. R. Grove, F.R.S Rev. Prof. B. Powell, F.R.S. Prof. M. Faraday, F.R.S Hugh E. Strickland, F.G.S... . Subject of Discourse The Principles and Construction of Atmospheric Railways, The Thames Tunnel. The Geology of Russia. The Dinornis of New Zealand. The Distribution of Animal Life in the ^gean Sea. The Earl of Rosse's Telescope. Geology of North America. The Gigantic Tortoise of the Siwalik Hills in India. Progress of Terrestrial Magnetism. Geology of Russia. Fossil Mammalia of the British Isles. Valley and Delta of the Mississippi. Properties of the Explosive substance discovered by Dr. Schonbein ; also some Researches of his own on the Decomposition of Water by Heat. Shooting Stars. Magnetic and Diamagnetic Pheno- mena. The Dodo {Bidus ineptus). Iviii REPORT 1885. Date and Place 1848. Swansea , 1849. Birmingham 1850. Edinburgh 1851. Ipswich .. 1852. Belfast 1853, Hull. 1854. Liverpool... 1855. Glasgow ... 1856. Cheltenham Lecturer 1857. Dublin.... 1858. Leeds .... 1859. Aberdeen. 1860. Oxford 1861. Manchester 1862. Cambridge 1863. Newcastle 1864. Bath 1865. Birmingham 1866. Nottingham John Percy, M.D., F.R.S W. Carpenter, M.D., F.R.S... . Dr. Faraday, F.K.S Rev. Prof. Willis, M.A., F.R.S. Prof. J. H. Bennett, M.D., F.R.S.E. Dr. Mantell, F.R.S Prof. R. Owen, M.D., F.R.S. G.B.Airy,F.R.S.,Astron. Royal Prof. G. G. Stokes, D.C.L., F.R.S. Colonel Portlock, R.E., F.R.S. Prof. J. Phillips, LL.D., F.R.S., F.G.S. Robert Hunt, F.R.S Prof. R. Owen, M.D., F.R.S. Col. E. Sabine, V.P.R.S Dr. W. B. Carpenter, F.R.S. Lieut.-Col. H. Rawlinson ... Col. Sir H. Rawlinson W. R. Grove, F.R.S Prof. W. Thomson, F.R.S. ... Rev. Dr. Livingstone, D.C.L. Prof. J. Phillips,LL.D.,F.R.S. Prof. R. Owen, M.D., F.R.S. Sir R. I. Murchison, D.C.L... . Rev. Dr. Robinson, F.R.S. ... Rev. Prof. Walker, F.R.S. ... Captain Sherard Osborn, R.N. Prof. W. A. Miller, M.A., F.R.S. G.B.Airy,F.R.S.,Astron.Royal Prof. Tyndall, LL.D., F.R.S. Prof. Odliug, F.R.S Prof. Williamson, F.R.S James Glaisher, F.R.S., Prof. Roscoe, F.R.S Dr. Livingstone, F.R.S. J. Beete Jukes, F.R.S. .. William Huggins, F.R.S. ... Dr. J. D. Hooker, F.R.S Subject of Discourse Metallurgical Operations of Swansea and its neighbourhood. Recent Microscopical Discoveries. Mr. Gassiot's Battery. Transit of diiferent Weights with varying velocities on Railways. Passage of tlie Blood through the minute vessels of Animals in con- nexion with Nutrition. Extinct Birds of New Zealand. Disi inct ion between Plants and Ani- mals, and tlieir changes of Form. Total Solar Eclipse of July 28, 1851. Recent discoveries intlie properties of Light. Recent discovery of Rock-salt at Carrickfergus, and geological and pract ical considerations connected with it. Some peculiar Phenomena in the Geohigy and Physical Geography of Yorkshire. The present state of Photography. Anthropomorphous Apes. Progress of researches in Terrestrial Magnetism. Characters of Species. Ass3Tian and P>abylonian Antiquities and Etlinology. Recent Discoveries in Assyi'ia and Babylonia, v^^ith the results of Cuneiform research up to the present time. Correlation of Plij'sical Forces. The Atlantic Telegraph. Recent Discoveries in Africa. The Ironstones of Yorkshire. The Fossil Mammalia of Australia. Geology of the Nortliern Highlands. Electrical Discharges in highly rarefied Media. Physical Constitution of the Sun. Arctic Discovery. Spectrum Analysis. The late Eclipse of the Sun. The Forms and Action of Water. Organic Chemistry. The Chemistry of the Galvanic Bal tery considered in relation to Dynamics. The Balloon Ascents made for the British Association. The Chemical Action of Light. Recent Travels in Africa. Probabilities as to the position and extent of the Coal-measures be- neath the red rocks of the Mid- land Counties. The results of Spectrum Analysis applied to Heavenly Bodies. Insular Floras. LIST OF EVENING LECTDBES. lis Date and Place 1867. Dundee. 1868. Norwich ... 1869. Exeter 1870. Liverpool... 1871. Edinburgh 1872. Brighton ... 1873. Bradford ... 1874. Belfast 1876. Bristol 1876. Glasgow ... 1877. Plymouth . 1878. Dublin 1879. Sheffield ... 1880. Swansea ... 1881. York. 1882. Southamp- ton. 1883. Southport 1884. Montreal... 1885. Aberdeen.. Lecturer Archibald Geikie, F.R.S Alexander Herschel, F.R.A.S. J. Fergiisson, F.E.S Dr. W. Odling, F.R.S Prof. J. Phillips, LL.D.,F.E.S. J. Norman Lockyer, F.R.S.... Prof. J. Tyndall, LL.D., F.R.S. Prof .W. J. Macquorn Eankine, LL.D., F.R.S. F. A. Abel, F.R.S E. B. Tylor, F.R.S Prof. P.Martin Duncan, M.B., TCI T> Q Prof. W.K. Clifford Subject of Discourse Prof. W. C.Williamson, F.R.S. Prof. Clerk Maxwell, F.R.S. Sir John Lubbock,Bart.,M.P., F.R.S. Prof. Huxley, F.R.S ■W.Spottiswoode,LL.D.,F.R.S. F. J. Bramwell, F.R.S Prof. Tait, F.R.S.E SirAVyville Thomson, F.R.S. W. Warington Smyth, M.A., F.R.S. Prof. Odling, F.R.S G. J. Romanes, F.L.S Prof. Dewar, F.R.S W. Crookes, F.R.S Prof. E. Ray Lankester, F.R.S. Prof. W. Boyd Dawkins, F.R.S. Francis Galton, F.R.S Prof. Huxley, Sec. R.S W. Spottiswoode, Press. R.S. Prof. Sir Wm. Thomson, F.R.S. Prof. H. N. Moseley, F.R.S. Prof. R. S. Ball, F.R.S Prof. J. G. McKendrick, F.R.S.E. Prof. O. J. Lodge, D.Sc Rev. W. H. DaUinger, F.R.S. Prof. W. G. Adams, F.R.S. .., John Murray, F.R.S.E The Geological Origin of the present Scenery of Scotland. The present state of knowledge re- garding Meteors and Meteorites. Archeology of the early Buddhist Monuments. Reverse Chemical Actions. Vesuvius. The Physical Constitution of the Stars and Nebulse. The Scientific Useof the Imagination. Stream-lines and Waves, in connec- tion with Naval Architecture. Some recent investigations and ap- plications of Explosive Agents. The Relation of Primitive to Modern Civilization. Insect Metamorphosis. The Aims and Instruments of Scien- tific Thouglit. Coal and Coal Plants. Molecules. Common Wild Flowers considered in relation to Insects. The Hypothesis that Animals are Automata, and its History. Tlie Colours of Polarized Light. Railway Safety Appliances. Force. The Cliallfngcr Expedition. The Physical Phenomena connected with the Mines of Cornwall and Devon. The new Element, Gallium. Animal Intelligence. Dissociation, or Modern Ideas of Chemical Action. Radiant Matter. Degeneration. Primeval Man. Mental Imagery. The Rise and Progress of Palason* tology. The Electric Discharge, its Forms and its Functions. Tides. Pelagic Life. Recent Researches on the Distance of the Sun. Galvani and Animal Electricity. Dust. The Modern Microscope in Re- searches on the Least and Lowest Forms of Life. The Electric Light and Atmospheric Absorption. The Great Ocean Basins. Ix REPORT — 1885. LECTURES TO THE OPERATIVE CLASSES. Date and Place Lecturer Subject of Discourse 1867. Dundee Prof. J. Tyndall, LL.D.,F.K.S. Matter and Force. 1868. Norwich ... Prof. Huxley, LL.D., F.E.S. A Piece of Chalk. 1869. Exeter Prof. Miller, M.D., F.E.S. ... Experimental illustrations of the modes of detecting the Composi- tion of the Sun and other Heavenly Bodies by the Spectrum. 1870. Liverpool... Sir John Lubbock, Bart.,M.P., F.K.S. Savages. 1872. Brighton ... W.Spottiswoode,LL.D.,F.R.S. Sunshine, Sea, and Sky. 1873. Bradford ... C. W. Siemens, D.C.L., F.R.S. Fuel. 1 874 Belfast Prof Odlino-. F.R.S The Discovery of Oxygen, A Piece of Limestone. X O 1 ^ t -^ v7 i. J. CuO Li ■•((•* 1875. Bristol Dr. W. B. Carpenter, F.R.S. 1876. Glasgow ... Commander Cameron, C.B., R.N. W. H. Preece A Journey through Africa. 1877. Plymouth... 1879 Sheffield Telegraphy and the Telephone. Electricity as a Motive Power. The North-East Passage. W E Avrton 1880. Swansea ... H. Seebohm, F.Z.S 1881. York Prof. Osborne Reynolds, Raindrops, Hailstones, and Snow- F.R.S. flakes. 1882. Southamp- John Evans, D.C.L. Treas. R.S. Unwritten History, and how to ton. read it. 1883. Southport Sir F. J. Bramwell, F.R.S. ... Talking by Electricity — Telephones. 1884. Montreal ... Prof. R.S. Ball, F.R.S Comets. 1885. Aberdeen... H. B. Dixon, M.A The Nature of Explosions. Ixi OFFICERS OF SECTIONAL COMMITTEES PRESENT AT THE. ABERDEEN MEETING. SECTION A. — MATHEMATICAL AND PHYSICAL SCIENCE. Fresiclent.—FToiessor G. Chrystal, M.A., F.R.S.E. Vice-Presidents.— ProkssoT C. Niven, F.R.S. ; Lord Rayleigh, F.R.S. ;. Professor A. Schuster, F.R.S. ; Professor G, G. Stokes, Sec.R.S. ; Professor Sir W. Thomson, F.R.S. Secretaries— R. E. Baynes, M.A. ; R. T. Glazebrook, F.R.S. ; Professor W. M. Hicks, F.R.S. (Becorder) ; Professor W. Ingram, M.A. SECTION B. — CHEMICAL SCIENCE. President.— Proiessov H. E. Armstrong, Ph.D., F.R.S., Sec.C.S. Vice-Presidents. — Professor Brazier, F.C.S. ; Professor A. Crum Brown, F.R.S. ; Professor Hartley, F.R.S. ; Professor H. McLeod, F.R.S. ; Professor W. A. Tilden, F.R.S. Secretaries. — Professor P. Phillips Bedson, D.Sc. {Becorder) ; H. B. Dixon, M.A. ; H. Forster Morley, D.Sc. ; W. J. Simpson, M.D. SECTION C. — GEOLOGY. PrmcZen^.— Professor J. W. Jndd, F.R.S., Sec.G.S. Vice-Presidents. — John Evans, Treas.R.S.; Rev. George Gordon, LL.D, ; T. F. Jamieson, LL.D. ; Rev. J. M. Joass, LL.D. ; Professor O. C. Marsh, M.A. ; Professor W. C. Williamson, F.R.S. Secretaries.— C. E. De Ranee, F.G.S. ; J. Home, F.R.S.E. ; J. J. H. Teall, F.G.S. ; W. Topley, F.G.S. {Recorder). SECTION D. — BIOLOGY. President.— PTo^esaov W. C. Mcintosh, M.D., LL.D., F.R.S. L. and E., F.L.S. Vice-Presidents. — Professor C. C. Babington, F.R.S. ; Professor I. Bayley Balfonr, F.R.S. ; Professor Cleland, F.R.S. ; Sir John Lubbock, Bart., F.R.S.; Professor J. S. Bnrdon Sanderson, F.R.S.; Pro- fessor W. Stirling, F.R.S.E. ; Professor Trail, F.L.S. Secretaries. — W. Heape ; J. McGi-egor- Robertson, M.B. ; J. Duncan Matthews, F.R.S.E. ; Howard Saunders, F.L.S. {Recorder) ; H.. Marshall Ward, M.A. Ixii REPORT — 1885. SECTION E. — GEOGRAPHY. Fresident.— General J. T. Walker, C.B., R.E., LL.D., F.R.S. Vice-Presidents. — Professor James Donaldson, F.R.S.E. ; Admiral Sir E. Ommanney, C.B,, F.R.S. ; Lieat.- Colonel R. L. Playfair; Dr. John Rae, F.R.S. Secretaries.— J. S. Keltie ; J. S. O'Halloran, F.R.G.S.; E. G. Raven- stein, F.R.G.S. (Recorder) ; Rev. G. A. Smith, M.A. SECTION F. — ECONOMIC SCIENCE AND STATISTICS. President. — Professor Henry Sidgwick, LL.D., Litt.D. Vice-Presidents. — Professor Adanison, LL.D. ; Dr. Alexander Bain ; Major P. G. Craigie ; Sir Richard Temple, Bart., G.C.S.I. .Secretaries. — Rev. W. Cunningham, B.D. ; Professor H. S. Foxwell, M.A. (Recorder) ; C. McCombie ; J. F. Moss. SECTION G. — MECHANICAL SCIENCE. President. — Benjamin Baker, M.Inst. C.E. Vice-Presidents. — W. H. Barlow, F.R.S. ; Sir James N. Douglass ; Pro- fessor James Thomson, F.R.S. ; Professor W. C. Unvvin. ■Secretaries. — A. T. Atchison, M.A. ; F. G. Ogilvie, M.A., B.Sc. ; E. Rigg, M.A. (Recorder) ; J. N. Shoolbred, B.A. SECTION H. — ANTHROPOLOGY. President. — Francis Galton, M.A., F.R.S., President of the Anthropo- logical Institute. Vice-Presidents. — Dr. Alexander Bain ; Professor D. J. Cunningham, M.D. ; Professor Flower, F.R.S. ; W. Pengelly, F.R.S. ; Professor Strnthers, M.D. ; Professor W. Turner, F.R.S. .Secretaries. — G. W. Bloxam, F.L.S. (Recorder) ; J. G. Garson, M.D. ; Walter Hurst, B.Sc. ; A. McGregor, M.D. Eh 12; o o o P3 05 ti CO <1 H w Ci o O O oo n; 'f C-. o O © O >a (>) lO O -f -t< t^ 00 -M t^ — CT5 re -+ -^ -t^ C^l ^1 CC C'l 1— I 13 -»^ cc 3 « g o a) ts (B ^ -" O -I «: *-^ C ft _o -r; ^^ 3 OT cc y3 ° Is o § So S 5 L^<i!h g o o p,- 0^ > 3 O O o o lO O o s ^ 2 00 5 a u p ^ o s n '5 a Qi r c? o t-H OJ •* (M «) fin -w i-i o o "a CO l-O 1-H ^ VJ ^ 0) <D ^ 0) 60 c (1% C O TO « o <u " « o 8 £ o <^ c5 o O O 05 CO pa tD "^ ^ ■-I • S -w 00 b^ OQ 1^ 2 t> « S ci I- g c3 -I H.S CO Ixiv EEPORT — 1885. Ta^le showing the AttendaTice and ReceipU Date of Meeting 1831, Sept. 27 .. 1832, June 19 .. 1833, June 25 .. 1834, Sept. 8 .. 1835, Aug. 10 .. 1836, Aug. 22 .. 1837, Sept. 11 .. 1838, Aug. 10 .. 183!), Aug. 26 .., 1840, Sept. 17 .. 1841, July 20 .. 1842, June 23 .. 1843, Aug. 17 .. 1844, Sept. 26 .. 1845, June 19 .. 1846, Sept. 10 .. 1847, June 23 .. 1848, Aug. 9 .. 1849, Sept. 12 .. 1850, July 21 .. 1851, July 2 .. 1852, Sept. 1 .. 1853, Sept. 3 .. 1854, Sept. 20 .. 1855, Sept. 12 .. 1856, Aug. 6 .. 1857, Aug. 26 .. 1858, Sept. 22 .. 1859, Sept. 14 .. 1860, June 27 .. 1861, Sept. 4 .. 1862, Oct. 1 .. 1863, Aug. 26 .. 1864, Sept. 13 .. 1865, Sept. 6 .. 1866, Aug. 22 .. 1867, Sept. 4 .. 1868, Aug. 19 .. 1869, Aug. 18 .. 1870, Sept. 14 .. 1871, Aug. 2 ., 1872, Aug. 14 .. 1873, Sept. 17 ., 1874, Aug. 19 . 1875, Aug. 25 . 1876, Sept. 6 . 1877, Aug. 15 . 1878, Aug. 14 . 1879, Aug. 20 . 1880, Aug. 25 . 1881, Aug. 31 . ] 882, Aug. 23 . 1883, Sept. 19 ., 1884, Aug. 27 . 1885, Sept. 9 . Where held Presidents York Oxford Cambridge Edinburgh Dublin Bristol Liverpool Newcastle-on-Tyne B irmingham Glasgow PljTnoiith Manchester Cork York Cambridge Southamijton Oxford Swansea Birmingham Edinburgh Ipswich Belfast Hull Liverpool Glasgow Cheltenham Dublin Leeds Aberdeen Oxford Manchester Cambridge Newcastle-on-Tyne Bath Birmingham Nottingham Dundee Norwich Exeter Liverpool Edinburgh Brighton Bradford ! Belfast ! Bristol Glasgow Plymouth Dublin Sheffield Swansea York Southampton Southport Montreal Aberdeen The Earl Fitzwilliam, D.C.L. The Rev. W. Buckland, F.R.S. The Rev. A. Sedgwick, F.R.S. Sir T. M. Brisbane, D.C.L The Rev. Provost Lloyd, LL.D. The Marquis of Lansdowne ... The Earl of Burlington, F.R.S. The Duke of Northumberland The Rev. W. Vernon Harcourt The Marquis of Breadalbane... The Rev. W. WnevfeU, F.R.S. The Lord Francis Egertou The Earl of Rosse, F.R.S The Rev. G. Peacock, D.D. ... Sir John F. W. Herschel, Bart. Sir Roderick I. i\Iurchison,Bart. Sir Robert H. Inglia, Bart The Marquis of Northampton The Rev. T. R. Robinson, D.D. Sir David Brewster, K.H G. B. Airy, Astronomer Royal Lieut.-General Saljine, F.R.S. William Hopkins, F.R.S The Earl of Harrowby, F.R.S. The Duke of Arayll, F.R.S. ... Prof. C. G. B. Daubeny, M.D. The Rev.Humphiev Lloyd, D.D. Richard Owen, M'D., D.C.L.... H.R.H. the Prince Consort ... I The Lord Wrottesley, M.A. .. WilliamFairbaim,LL.D.,F.R.S. I The Rev. Prof essor Willis, M.A. Sir William G.Armstrong, C.B. Sir Charles Lyell, Bart., M.A. 1 Prof. J. Phillips, M.A., LL.D. I William R. Grove, Q.C., F.R.S. I The Duke of Buccleuch,K.C.B. 1 Dr. Joseph D. Hooker, F.R.S. i Prof. G. G. Stokes, D.C.L Prof. T. H. Huxley, LL.D Prof. Sir W. Thomson, LL.D. Dr. W. B. Carpenter, F.R.S. ... Prof. A. W. Williamson, F.R.S. Prof. J. Tyndall, LL.D., F.R.S. SirJohnHawkshaw,C.E.,F.R.S. Prof. T. Andrews, M.D., F.R.S. Prof. A. Thomson, M.D., F.R.S. W. Spottiswoode, M.A., F.R.S. Prof.G. J. Allman, M.D., F.R.S. A. C. Ramsay, LL.D., F.R.S.... Sir John Lubbock, Bart., F.R.S. Dr. C. W. Siemens, F.R.S Prof. A. Cayley, D.C.L., F.R.S. Prof. Lord Rayleigh, F.R.S. ... Sir Lyon Playf air, K.C.B.,F.E.S. Old Life Members 169 303 109 226 313 241 314 149 227 235 172 164 141 238 194 182 236 222 184 286 321 239 203 287 292 207 167 196 204 314 246 245 212 162 239 221 173 201 184 144 272 178 203 235 225 ATTENDANCE AND RECEIPTS AT ANNUAL MEETINGS. Ixv Innual Meetings of the Association. Attended by Amount Sums paid on Account of Grants for Scientific Purposes Old anual mbers New Annual Members Asso- ciates Ladies For- eigners Total received during the Meeting Year ... ... ... 353 1831 1832 ... ... ... ... 900 1298 1833 18.34 1835 £20 167 ••• ... lioo* ... 1350 1840 2400 435 922 12 6 932 2 2 1836 1837 1838 46 ill 376 185 190 22 39 40 25 "eo* 331* 160 260 172 196 203 197 34 40 28 35 36 53 15 1438 1353 891 1315 1079 857 1320 819 1595 11 1546 16 4 1235 10 11 1449 17 8 1565 10 2 981 12 8 831 9 9 685 16 208 5 4 275 1 8 1839 1840 1841 1842 1843 1844 1845 1846 1847 1848 75 '33t '"at 407 270 495 376 71 45 94 65 197 54 £m"6'o 93 33 447 237 22 1071 963 159 19 6 1849 128 42 510 273 44 1241 1085 345 18 1850 61 47 244 141 37 710 620 391 9 7 1851 63 60 510 292 9 1108 1085 304 6 7 1852 56 57 367 236 6 876 903 205 1853 121 121 76.5 524 10 1802 1882 380 19 7 1854 142 101 1094 543 26 2133 2311 480 16 4 1855 104 48 412 346 9 1115 1098 734 13 9 1856 156 120 900 569 26 2022 2015 507 15 4 1857 111 91 710 509 13 1698 1931 618 18 2 1858 125 179 1206 821 22 2564 2782 684 11 1 1859 177 59 636 463 47 1689 1604 766 19 6 1860 184 125 1589 791 15 3138 3944 1111 5 10 1861 150 57 433 242 25 1161 1089 1293 16 6 1862 154 209 1704 1004 25 3335 3640 1608 3 10 1863 182 103 1119 1058 13 2802 2965 1289 15 8 1864 215 149 766 508 23 1997 2227 1591 7 10 1865 J18 105 960 771 11 2303 2469 1750 13 4 1866 193 118 1163 771 7 2444 2613 1739 4 1867 J26 117 720 682 45| 2004 2042 1940 1868 229 107 678 600 17 1856 1931 1622 1869 503 195 1103 910 14 2878 3096 1572 1870 511 127 976 754 21 2463 2575 1472 2 6 1871 280 80 937 912 43 2533 2649 1285 1872 237 99 796 601 11 1983 2120 1685 1873 532 85 817 630 12 1951 1979 1151 16 1874 307 93 884 672 17 2248 2397 960 1875 531 185 1265 712 25 2774 3023 1092 4 2 1876 238 59 446 283 11 1229 1268 1128 9 7 1877 290 93 1285 674 17 2578 2615 725 16 6 1878 239 74 629 349 13 1404 1425 1080 11 11 1879 171 41 889 147 12 915 899 731 7 7 1880 U13 176 1230 514 24 2557 2689 476 3 1 1881 253 79 516 189 21 1253 1286 1126 1 11 1882 !30 323 952 841 5 2714 3369 1083 3 3 1883 517 219 826 74 26&60H.§ 1777 1538 1173 4 1884 532 122 1053 447 6 2203 2256 1385 1885 dies were not admitted ty purchased Tickets until 1843. + Tickets of Admission to Sections only, cludmg Ladies. § Fellows of the American Association wer» admitted as Honorary Members for this Meeting d OFFICERS AND COUNCIL, 1885-86. PRESIDENT. The Right Hon. SIR LYON PLATFAIR, K.C.B., M.P., Ph.D., LL.D., F.R.S.L.&E., F.C.S. VICE-PRESIDENTS. His Grace the Duke o£ Richmond and Gordon, K.G., D.C.L., Cliaucellor of tlie University of Aberdeen. Tlie Right Hon. the Earl of Aberdeen, LL.D., Lord-Lieutenant of Aberdeenshire. The Right Hon. the Earl of Crawkord and Balcarres, M.A., LL.D., F.R.S., F.R.A.S. James Matthews, Esq., Lord Provost of the City of Aberdeen. Professor Sir William Thomson, M.A., LL.D., F.R.S. L. & E., F.R.A.S. Alexander B.un, Esq., M.A., LL.D.. Rector of the University of Aberdeen. Professor W. H. Flower, LL.D., F.R.S., F.L.S., F.G.S., Pres. Z.S., Director of the Natural History Museum, London. Professor John Struthers, M.D., LL.D. PRESIDENT ELECT. Sir William Dawson, C.M.G., JI.A.. LL.D., F.R.S. , P.G.S., Principal of McGill College, Montreal, Canada. VICE-PRESID The Right Hon. the Earl op Bradford, Lord- Lieutenant of Shropsliire. The Riglit Hon. Lord Leioh, D.C.L., Lord-Lieu- tenant of Warwicksiiire. The Bight Hon. LoiiD Norton, K.C.M.G. The Right Hon. Loud Wrottesley, Lord-Lieu- tenant of Staffordshire. ENTS ELECT. The Riglit Rev. the Lord Bishop of Worcester, D.D. THOJU.S Martineau, Esq., Mayor of Birmingham. Professor G. G. Stokes, D.C.L., LL.D., Pres. R.S. Professor W. A. Tilden, D.Sc, F.R.S., F.C.S. Rev. A. R. Vardy, M.A. Rev. A. W. Watson, D.Sc, F.R.S. LOCAL SECRETARIES FOR THE MEETING AT BIRMINGHAM. J. Barh-UI Carslake, Esq. | Rev. H. W. Crosskey, LL.D., F.G.S. | Charles J. Hart, Esq. LOCAL TREASURER FOR THE MEETING AT BIRMINGHAM. J. D. Goodman, Esq. ORDINARY MEMBERS Abney. Capt. W. DE W., F.R.S. Ball, Professor R. S., F.R.S. Bateman, J. F. La Trobe. Esq., F.R.S. BL.4.NF0RD, W. T., Esq., F.R.S. Bramwell, Sir F. J.. F.R.S. Crookes, W., Esq., F.R.S. Dawkins, Professor W. Boyn, F.R.S. De La Rue, Dr. Warren, F.R.S. Dewar, Professor J., F.R.S. Flower, Professor W. H., F.R.S. Gl.\dstoxe, Dr. J. H., F.R.S. Gl.u.sheb, J. W. L., Esq., F.R.S. God WIN- Austen, Lieut.-Col. H. H., F.R.S. OF THE COUNCIL. Hawkshaw, J. Clarke, Esq., F.G.S. Hknrici, Professor 0., F.R.S. Hughes, Professor T. McK., F.G.S. Martin, J. B., Esq.. F.S.S. M'Leod, Professor H., F.R.S. MosKLEV. Professor H. N., F.R.S. Ojimanxey, Admiral Sir E., C.B., F.R.S. Pengelly, W., Esq., F.R.S. Perkin, Dr. W. H., F.R.S. SORBY, Dr. H. C. F.R.S. Temple, Sir R., Bart. G.C.S.I. Thiselton-Dyer, W. T., Esq., C.M.G., F.B.S. GENERAL SECRETARIES. Capt. Douglas Galton, C.B., D.C.L., LL.D., F.R.S., F.G.S., 12 Chester Street, London, S.\7. A. G. Vernon Harcourt, Esq., M.A., LL.D., F.R.S., F.C.S., Cowley Grange. Oxford. SECRETARY. Arthur T. Atchison, Esq., M.A., 22 Albemarle Street, London, W. GENERAL TREASURER. Professor A. W. Williamson, Ph.D., LL.D., F.R.S., F.C.S., University College, London, W.C. EX-OFFICIO MEMBERS OF THE COUNCIL. The Trustees, the President and President Elect, tlie Presiilents of former years, the Vice-Presidents and Vice-Presidents Elect, the General and Assistant General Secretaries for the present and former yeai-s, the Secretary, the Genpral Treasurers for the present and former years, and the Local Treasurer and Secretaries for the eusuuig Meeting. TRUSTEES (PERMANENT). Sir John Lubbock, Bart.. MP., D.C.L., LL.D., F.R.S., Pres. L.S. The Right Hon. Lord Rayleigh, M.A., D.C.L., LL.D., Sec. R.S., F.R.A.S. The Right Hon. Sir Lyon Playfair, K.C.B., M.P., Ph.D., LL.D., F.R.S. PRESIDENTS OF FORMER TEARS. The Duke of Devonshire, K.G. Sir G. B. Airy, K.C.B., F.R.S. The Duke of Argyll, K.G., K.T. Sir Richard Owen, K.C.B., F.R.S. Sir W. G. Armstrong, C.B., LL.D. Sir William R. Grove, F.R.S. Sir Joseph D. Hooker, K.C.S.I. Prof. Stokes, D.C.L., Pres. R.S. Prof. Huxley, LL.D., F.R.S. Prof. Sir Wm. Tliomson, LL.D. Prof. Williamson, Ph.D., F.R.S. Prof. Tvndall, D.C.L., F.R.S. Sir John Hawkshaw, F.R.S. Prof. AUman, M.D., F.R.S. Su- A. C. Ramsay, LL.D., F.R.S. Sir John Lubbock, Bart., F.R.S. Prof, Cayley, LL.D., F.R.S. Lord Rayleigh, D.C.L., Sec. R.S. P. Galton. Esq., F.R.S. Dr.T. A. Hirst, F.R.S. GENERAL OFFICERS OP FORMER TEARS. I Dr. Michael Foster, Sec. R.S. | P. L. Sclater, Esq., Ph.p.,_P.R.S. , GeorgeGriffith, Esq., M.A,, F.C.S. I Prof. Bonney, D.Sc, F.R.S. John Evans, Esq., D.C.L., F.R.S. AUDITORS. I W. Huggins, Esq., D.C.L., F.R.S. I W. H. Preece, Esq., F.R.S. Ixvii REPORT OF THE COUNCIL. Heport of the Council for the year 1884-85, presented to the General Committee at Aberdeen, on Wednesday, September 9, 1885. The Council have received reports during the past year from the Oeneral Treasurer, and his accounts for the year will be laid before the General Committee this day. Since the Meeting at Montreal, the following have been elected Corresponding Members of the Association : — Bowditch, Prof. H. P. Kikuchi, Prof. Dairoku. Brusb, Prof. G. J. Michelson, A. A. Gibbs, Prof. J. Willard. Newcomb, Prof. Simon. Gibbs, Prof. Wolcott. Powell, Major J. W. Greely, Lieut. A. W. Ray, Captain P. H. Jackson, Prof. C. Loring. Thurston, Prof. R. H. The Council have nominated Professor Struthers, M.D., LL.D., to he a Vice-President at the Meeting at Aberdeen. Soon after the commencement of the present year, Professor Bonney, -the Secretary, informed the Council that a considerable increase in the endowment of his Professorship at University College would demand that in future a larger share of his time should be devoted to teaching. As unfortunately the state of his health for some months past had pointed to the need of diminishing rather than increasing his work, he regretted that he would be unable to offer himself for re-election at the present Meeting. The Council received this announcement with very great regret." Professor Bonney not only brought to the office of Secretary a leading scientific position, but also combined with this advantage great energy, zeal, and discretion. It was largely due to his powers of organi- sation and tact that the exceptional and grave difficulties which attended the holding of last year's Meeting at Montreal were surmounted, and it was brought to a successful issue. The Council have nominated Mr. A. T. Atchison M.A., who for some years past has rendered most efficient assistance as one of the Secretaries of Section G, to the office of Secretary, vacated by Professor Bonney. During the present year the Council have considered the stipend paid to Mr. Stewardson, the Clerk of the Association, and the amount assigned to the General Treasurer to enable him to obtain such assistance as may be requisite. Mr. Stewardson was engaged in the year 1873 at a salary of 120Z., which was subsequently augmented to VSOl. The Council now recommend that for the present year it be raised to 135Z., and be subsequently increased (subject to the usual conditions) by a sum of 51. at the end of each three years till a maximum of 160L be reached ; also that the yearly sum assigned to the General Treasurer be increased from 501. to 601. d 2 Ixviii KEPORT — 1885. On meeting again in Great Britain, the Council venture to express to the General Committee their belief that the anticipations of a successful meeting, expressed in the Report presented at Montreal, have been fully justified by the results, and once more give utterance to the gratitude, which must be felt by all who visited Canada, for the liberal hospitality and cordial reception which welcomed them there. It will be long before this visit is forgotten, or the stimulus, which its exceptional circumstances gave to the energy and life of the Association, ceases to be felt. Towards the close of that Meeting the happy idea occurred to several members of the Association that it would be an appropriate memorial of the visit of the British Association to found a Medal at McGill University, to be given annually for proficiency in Applied Science. The idea, once started, was warmly espoused, and a subscription list was opened, with Lord Rayleigh, the President, as Treasurer, and Messrs. W. Topley and H. T. Wood as Secretaries. The result has been that a sum of about 5001. will be transmitted to the authorities of the McGill University for invest- ment. This will enable them to offer, as an annual prize, a Gold Medal and a sum of money. The first award has already been made. The Council, acting under the powers conferred upon them by the General Committee on Nov. 11, 1884, have instructed Mr. Wyon to prepare, at the cost of the Association, a suitable die for the Medal. The Council, in virtue of the powers conferred upon them by the General Committee at Montreal, in regard to the report concerning Corresponding Societies, have formed the Corresponding Societies' Committee. The Report of the Committee will be presented, and a con- ference of Delegates, appointed under the new rules, will be held during the present meeting. The following resolutions were referred by the General Committee to the Council for consideration and action, if desirable : — ' That the Council of the Association be requested to communicate with the Government of the Dominion of Canada in order (1) to call the attention of the Government to the absence of trustworthy informa- tion concerning the tides of the Gulf of St. Lawrence and the adjoining Atlantic coast, and to the dangers which thence arise to the navigation ; (2) To urge upon the Government the importance of obtaining accurate and systematic tidal observations, and of tabulating and reducing the results by the scientific methods elaborated by Committees of the Associa- tion ; and (3) to suggest the immediate establishment of a sufficient eeries of observing stations on the coast of the Dominion.' A memorial in accordance with the above resolution was adopted by the Council and forwarded to the Government of the Dominion of Canada. To this a reply was received from the Canadian Minister of Marine, expressing regret that the Dominion Government were unable at the present time to undertake a special sui'vey of the tides and currents in the Gulf of St. Lawrence. The Council, however, are not without hope that the proposed observations may be regarded as deferred rather than as refused. ' That the Council memorialise the Canadian Government as to the urgent necessity of encouraging investigation and publication of reports with respect to the physical characters, languages, social, industrial, and artistic condition of the native tribes of the Dominion.' A memorial in accordance with the above was also adopted by the ■Council and forwarded to the Government of the Dominion of Canada. REPORT OF THE COUNCIL. Ixix The receipt of this was acknowledged, and the Conncil were informed that it would be duly considered by the Dominion Government. ' That the attention of the Council be drawn to the advisability of communicating with the Admiralty for the purpose of urging on them the importance of the employment of the Harmonic Analysis in the Reduction of Admiralty Tidal Observations.' The above recommendation was duly considered, but the Council, while fully conscious of the importance of the subject, deemed the time inopportune for pressing the matter on the attention of the Admiralty. ' That the Council be requested to examine the feasibility of insti- tuting a scheme for pi'omoting an International Scientific Congress, to meet at intervals in different countries, and to report thereon to the General Committee at the next meeting of the Association.' This most important question has been very fully considered by the Council during the past year. The importance of such a Congress can hardly be doubted ; at the same time there are many serious difficulties in devising a practical scheme, and many considerations to be taken into account, before it would be prudent to undertake so great a departure from the ordinary procedure of the Association, as would be involved by such schemes as have seemed most feasible. The following is a brief history of what has been done : At the conclusion of the Montreal Meeting a Committee of the Council (of which Mr. Vernon Harcourt, the General Secretary, was a member) took the opportunity of being present at the meeting of the American Association at Philadelphia to confer with some members of the Committee in America, from whom the latest and most definite proposal of an International Scientific Association has emanated. After returning to England, a letter was received by Mr. Vernon Harcourt from Dr. S. C. Minot, Secretary to the above Committee, which was laid before a Committee of the Council. As a result of their consideration of this letter, the Secretary entered into an informal correspondence with Dr. C. S. Minot. The intent of this correspondence was to bring about an exchange of views and a discussion of certain difficulties which pre- sented themselves at first sight, and as it, in effect, contains the outline of a scheme, the Council (with Dr. Minot's permission) have resolved to place it, together with extracts from his letter to Mr. Vernon Harcourt, in the hands of the General Committee. Copies of it are accordingly distributed with this Report. The Council, in the next place, deemed it desirable to ascertain what support the proposal of a joint meeting of the British Association and of the International Scientific Association, in the suggested rudimentary form, would meet with from the more important scientific societies in London ; for, without their favourable countenance and the permission to use the rooms of such as were couveniently situated, the project would necessarily be abortive. A circular was accordingly ad- dressed to a number of the London scientific societies, with the result that out of 29 societies which sent answers, three expressed their inability, in consequence of formal difficulties, to reply at present ; two were opposed to the scheme ; five were favourable ; and the rest were not hostile. It should, however, be remarked, that while a willingness to lend rooms was very generally shown, any approbation of the scheme was expressed in very guarded terms, and amounted, in the majority of cases, to little more than a non-expression of disapproval. In these circum- stances the Council invite the General Committee to take the matter into Ixx REPORT — 1885. tlieir consideration duriDg the Aberdeen Meeting, and suggest that the second meeting of the General Committee would be the most convenient opportunity for a discussion. One vacancy in the Council has been caused by the lamented death of Dr. Gwyn Jeffreys ; another by the resignation of Prof. Prestwich ; it follows, therefore, that in accordance with the rule, three other members will retire. The retiring members will be : — Sir F. J. Evans. Prof. W. G. Adams. The Right Hon. G. Sclater-Booth. The Council recommend the re-election of the other ordinary Members of Council, with the addition of the gentlemen whose names are distin- guished by an asterisk in the following list : — Abney, Capt. W. de W., F.R.S. Ball, Prof. R. S., F.R.S. Bateman, J. F. La Trobe, Esq., F.R.S. *Blanford, W. T., Esq., F.R.S. Bramwell, Sir F. J., F.R.S. *Crookes, W., Esq., F.R.S. Dawkins, Prof. W. Boyd, F.R.S. De La Rue, Dr. Warren, F.R.S. Dewar, Prof. J., F.R.S. Flower, Prof. W. H., F.R.S. Gladstone, Dr. J. H., F.R.S. Glaisher, J. W. L., Esq., F.R.S. Godwin-Austen, Lieut.-Col. H. H., F.R.S. Hawkshaw, J. Clarke, Esq., F.G.S. Henrici, Prof. O., F.R.S. Hughes, Prof. T. McK., F.G.S. *Martin, J. B., Esq., F.S.S. *M'Leod, Prof. H., F.R.S. Moseley, Prof. H. N., F.R.S. Ommanney, Admiral Sir E., C.B., F.R.S. Pengelly, W., Esq., F.R.S. Perkin, Dr. W. H., F.R.S. Sorby, Dr. H. C, F.R.S. Temple, Sii- R., Bart., G.C.S.I. •Thiselton-Dyer, W. T., Esq.,. C.M.G., F.R.S. Ixxi Recommendations adopted by the General Committee at the Aberdeen Meeting in September 1885. [When Committees axe appointed, the Member first named is regarded as the Secretary, except there is a specific nomination.] Involving Grants of Money. That Professor G. Carey Foster, Sir William Thomson, Professor Ayrton, Professor J. Perry, Professor W. G. Adams, Lord Rayleigh, Dr. 0. J. Lodge, Dr. Johu Hopkinson, Dr. A. Muirhead, Mr. W. H. Preece, Mr. Herbert Taylor, Professor Everett, Professor Schuster, Dr. J. A. Fleming, Professor G. F. Fitzgerald, Mr. R. T. Glazebrook, Professor Chrystal, Mr. H. Tomlinson, Professor W. Garnett, Professor J. J. Thomson, and Mr. TV". N. Shaw be reappointed a Committee for the purpose of constructing and issuing practical Standards for use in Electrical Measurements ; that Mr. Glazebrook be the Secretary, and that the sum of 40/. be placed at their disposal for the purpose. That Professor Balfour Stewart, Professor Schuster, Professor Stokes, Mr. G. Johnstone Stoney, Professor Sir H. E. Roscoe, Captain Abney, and Mr. G. J. Symons be reappointed a Committee for the purpose of con- sidering the best methods of recording the direct intensity of Solar Eadia- tion ; that Professor Balfour Stewart be the Secretary, and that the un- expended sum of 20Z. be placed at their disposal for the purpose. That Professor Balfour Stewart (Secretary), Mr. Knox Laughton, Mr. G. J. Symons, and Mr. R. H. Scott be reappointed a Committee, with power to add to their number, for the purpose of co-operating with Mr. E. J. Lowe in his project of establishing a Meteorological Observatory near Chepstow on a permanent and scientific basis, and that the unex- pended sum of 25Z. be again placed at their disposal for the purpose. That Professor G. H. Darwin, Sir W. Thomson, and Major Baird be a Committee for the purpose of preparing instructions for the practical work of Tidal Observation ; that Professor Darwin be the Secretary, and that the sum of oOl. be placed at their disposal for the purpose. That Professors Balfour Stewart and Sir W. Thomson, Sir J. H. Lefroy, Sir Frederick Evans, Professor G. H. Darwin, Professor G. Chrystal, Professor S. J. Perry, Mr. C. H. Carpmael, Professor Schuster, Mr. G. M. Whipple, and Captain Creake be reappointed a Committee for the purpose of considering the best means of comparing and reducing Magnetic Observations ; that Professor Balfour Stewart be the Secretary, and that the sum of 40Z. be placed at their disposal for the purpose. That Professor G. Forbes, Captain Abney, Dr. J. Hopkinson, Professor W. G. Adams, Professor G. C. Foster, Lord Rayleigh, Mr. Preece, Professor Schuster, Professor Dewar, Mr. A. Vernon Har- court. Professor Ayrton, and Sir James Douglass be reappointed a Com- mittee for the purpose of reporting on Standards of Light ; that Professor G. Forbes be the Secretary, and that the sum of 201. be placed at their disposal for the purpose. Ixxii EEPORT — 1885. That Professor Crura Brown, Mr. Milne-Home, Mr. John Murray, and Mr. Bnchan be reappointed a Committee for the purpose of co- operating with the Scottish Meteorological Society in making meteoro- logical observations on Ben Nevis ; that Professor Crum Brown be the Secretary, and that the sum of lOOZ. be placed at their disposal for the purpose. That Professors Armstrong, Lodge, and Sir William Thomson, Lord Rayleigh, Professors Schuster, Poynting, J. J. Thomson, Fitzgerald, Crum. Brown, Ramsay, Frankland, Tilden, and Hartlev, Captain Abney, Messrs. W. N. Shaw, H. B. Dixon, J. T. Bottomley, W. Crookes, and Shelford Bidwell, and Dr. Fleming be a Committee for the purpose of considering the subject of Electrolysis in its Physical and Chemical bearings ; that Professor Armstrong be the Chemical Secretary and Professor Lodge the Physical Secretary, and that the sum of 20Z. be placed at their disposal for the purpose. That Professors McLeod and Ramsay and Mr. W. A. Shenstone be a Committee for the further investigation of the Influence of the Silent Discharge of Electricity on Oxygen and other gases ; that Mr. W. A. Shenstone be the Secretary, and that the sum of 20Z. be placed at their disposal for the purpose. That Professors Williamson, Dewar, Frankland, Crum Brown, Odling, and Armstrong, Drs. Hugo Miiller, A. G. Vernon Harcourt, F. R. Japp, and H. Forster Morley, and ]\Iessrs. C. E. Groves, J. Millar Thomson, V. H. Veley, and H. B. Dixon be reappointed a Committee for the purpose of drawing up a statement of the varieties of Chemical Names which have come into use, for indicating the causes which have led to their adoption, and for considering what can be done to bring about some convergence of the views on Chemical Nomenclature obtaining among English and foreign chemists ; that Mr. H. B. Dixon be the Secretary, and that the sum of bl. be placed at their disposal for the purpose. That Mr. W. T. Blanford, Professor J. W. Judd, and Messrs. W. Car- ruthers, H. Woodward, and J. S. Gardner be reappointed a Committee for the purpose of reporting on the Fossil Plants of the Tertiary and Secondary Beds of the United Kingdom ; that Mr. J. S. Gardner be the Secretary, and that the sum of 20L be placed at their disposal for the purpose. That Professor T. McK. Hughes, Dr. H. Hicks, Dr. H. Woodward, and Messrs. E. B. Luxmoore, P. Pennant, and Edwin Morgan be a Com- mittee for the purpose of exploring the Caves of North Wales ; that Dr. H. Hicks be the Secretary, and that the sum of 251. be placed at their disposal for the purpose. That Mr. R. Etheridge, Mr. T. Gray, and Professor John Milne be reappointed a Committee for the purpose of investigating the Volcanic Phenomena of Japan ; that Professor John Milne be the Secretary, and that the sum of 501. be placed at their disposal for the purpose. That Messrs. R. B. Grantham, C. E. De Ranee, J. B. Redman, W. Topley, W. Whitaker, and J. W. Woodall, Major-General Sir A. Clarke, Admiral Sir E. Ommanney, Sir J. N. Douglass, Captain Sir F. J. O. Evans, Captain J. Parsons, Captain W. J. L. Wharton, Professor J. Prestwich, and Messrs. E. Fasten, J. S. Valentine, and L. F. Vernou Harcourt be reappointed a Committee for the purpose of inquiring into the Rate of Erosion of the Sea-coasts of England and Wales, and the Influence of the Artificial Abstraction of Shingle or other Material in that RECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE. Ixxiii Action ; that Messrs. De Ranee and Topley be tlie Secretaries, and that the sum of 20?. be placed at their disposal for the purpose. That Messrs. H. Bauerman, F. W. Rndler, J. J. H. Teall, and H. J. Johnston-Lavis be reappointed a Committee for the purpose of investi- gating the Volcanic Phenomena of Vesuvius and its neighbourhood ; that Mr. H. J. Johnston-Lavis be the Secretary, and that the sum of 30?. be placed at their disposal for the purpose. That Dr. J. Evans, Professor W. J. Sollas, Dr. G- J. Hinde, and Messrs. W. CaiTuthers, R. B. Newton, J. J. H. Teall, F. W. Rudler, W. Topley, W. Whitaker, and E. Wethered be a Committee for the purpose of carry- ing on the Geological Record ; that Mr. W. Topley be the Secretary, and that the sum of 100?. be placed at their disposal for the purpose. That Mr. R. Etheridge, Dr. H. Woodward, and Professor T. R. Jones be reappointed a Committee for the purpose of reporting on the Fossil Phyllopoda of the Palseozoic Rocks ; that Professor T. R. Jones be the Secretary, and that the sum of 15?. be placed at their disposal for the purpose. Tbat Mr. Stainton, Sir John Lubbock,' and Mr. McLachlan be a Committee for the purpose of continuing a Record of Zoological Litera- ture ; that Mr. Stainton be the Secretary, and that the sum of 100?. be placed at their disposal for the purpose. That Mr. John Murray, Professor Cossar Ewart, Professor Alleyne Nicholson, Professor Mcintosh, Professor Young, Professor Struthers, and Professor McKendrick be reappointed a Committee for the purposes of a Marine Biological Station at Granton, Scotland ; that Mr. John Murray be the Secretary, and that the sum of 75?. be placed at their dis- posal for the purpose. That Professor Ray Lankester, Mr. P. L. Sclater, Professor M. Foster, Mr. A. Sedgwick, Professor A. M. Marshall, Professor A. C. Haddon, Professor Moseley, and Mr. Percy Sladen be reappointed a Committee for the purpose of arranging for the occasional occupation of a table at the Zoological Station at Naples ; that Mr. Percy Sladen be the Secretary, and that the sum of 50?. be placed at their disposal for the purpose. That Professor Cleland, Professor McKendrick, Professor Ewart, Professor Stirling, Professor Bower, Dr. Cleghorn, and Professor Mcintosh be a Committee for the purpose of continuing the Researches on Food Fishes and Invertebrates at the Marine Laboratory, St. Andrews ; that Professor Mcintosh be the Secretary, and that the sum of 75?. be placed at their disposal for the purpose. That Mr. J. Cordeaux, Mr. J. A. Harvie-Brown, Professor Newton, Mr. W. Eagle Clarke, Mr. R. M. Barrington, and Mr. A. G. More be appointed a Committee for the purpose of obtaining (with the consent of the Master and Elder Brethren of the Trinity House and the Commis- sioners of Northern and Irish Lights) observations on Migration at Lighthouses and Lightvessels, and of reporting on the same ; that Mr. J. Cordeaux be the Secretary, and that the sum of 30?. be placed at their disposal for the purpose. That Professor Cleland, Professor McKendrick, and Dr. McGregor- Robertson be a Committee for the purpose of investigating the Mechanism of the Secretion of Urine ; that Dr. McGregor- Robertson be the Secretary, and that the sum of 10?. be placed at their disposal for the purpose. That General J. T. Walker, Sir J. H. Lefroy, Lieut.- Colonel Godwin- Ixxiv REPORT — 1885. Austen, Mr. W. T. Blanford, Mr. Sclater, Mr. Carruthers, Mr. Thiselton- Dyer, Professor Strnthers, Mr. G. W. Bloxam, Mr. H. W. Bates, Lord Alfred Churcliill, Mr. F. Galton, Mr. J. S. O'Halloran, Mr. Coutts Trotter, and Professor Moseley be a Committee for the purpose of furthering the Exploration of New Guinea, by making a grant to Mr. Forbes for the purposes of his Expedition ; that Mr. H. W. Bates be the Secretary, and that the sum of 150/. be placed at their disposal for the purpose. That General J. T. Walker, Sir J. H. Lefroy, Sir William Thomson, Mr. Alexander Buchan, Mr. J. Y. Buchanan, Mr. John Murray, Dr. Rae, Mr. H. W. Bates, and Captain W. J. Dawson be a Committee for the purpose of organising a systematic investigation of the Depth of the per- manently Frozen Soil in the Polar Regions, its geographical limits, and relation 'to the present Pole of greatest cold ; that Mr. H. W. Bates be the Secretary, and that the sum of 51. be placed at their disposal for the purpose. That Professor Sidgwick, Professor Foxwell, the Rev. W. Cunning- ham, and Professor Munro be a Committee for the purpose of inquiring into the Regulation of Wages under the Sliding Scales ; that Professor Munro be the Secretary, and that the sum of 10/. be placed at their dis- posal for the purpose. That Mr. W. H. Barlow, Professor J. Thomson, Captain D. Galton, Mr. B. Baker, Professor W. C. TJnwin, Professor A. B. W. Kennedy, Mr. C. Barlow, Mr. A. T. Atchison, and Professor H. S. Hele Shaw be a Committee for the purpose of obtaining information with reference ta the Endurance of Metals under repeated and varying stresses, and the proper working stresses on Railway Bridges and other structures subject to varying loads ; that Mi\ A. T. Atchison be the Secretary, and that the sum of 10/. be placed at their disposal for the purpose. That Dr. Garson, Mr. Pengelly, Mr. P. W. Rudler, and Mr. _G. W.. Bloxam be a Committee for the purpose of investigating the Prehistoric Race in the Greek Islands ; that Mr. Bloxam be the Secretary, and. that the sum of 20^. be placed at their disposal for the purpose. That Dr. E. B. Tylor, Dr. G. M. Dawson, General Sir J. H. Lefroy, Dr. Daniel Wilson, Mr. R. G. Haliburton, and Mr. George W. Bloxam be reappointed a Committee for the purpose of investigating and publishing reports on the physical characters, languages, and industrial and social condition of the North- Western Tribes of the Dominion of Canada ; that Mr. Bloxam be the Secretary, and that the sum of 50/. be placed at their disposal for the purpose. That Mr. Francis Galton, Dr. Beddoe, Mr. Brabrook, Professor Cunningham, Professor Flower, Mr. J. Park Harrison, Professor A. Macalister, Dr. Muirhead, Mr. F. W. Rudler, Professor Thane, and Dr. Garson be reappointed a Committee for the purpose of defining the Racial Characteristics of the Inhabitants of the British Isles ; that Dr. Garson be the Secretary, and that the sum of 10/. be placed at their disposal for the purpose. Not involving Grants of Money. That Mr. James N. Shoolbred and Sir William Thomson be reap- pointed a Committee for the purpose of reducing and tabulating the Tidal Observations in the English Channel made with the Dover tide-gauge, EECOMMENDATIOMS ADOPTED BT THE GENERAL COMMITTEE. IxxV and of connecting them with observations made on the French coast ; and that Mr. Shoolbred be the Secretary. That Professor Barrett, Professor Fitzgerald, and Professor Balfour Stewart be a Committee for the pnrpose of reporting on the Molecular Phenomena attending the Magnetisation of Iron ; and that Professor Barrett be the Secretary. That Professor G. H. Darwin and Professor J. C. Adams be reap- pointed a Committee for the Harmonic Analysis of Tidal Observations ; and that Professor Darwin be the Secretary. That Mr. John Murray, Professor Schuster, Sir William Thomson, Professor Sir H. B. Roscoe, Professor A. S. Herschel, Captain W. de W. Abney, Professor Bonney, Mr. R. H. Scott, and Dr. J. H. Gladstone be reappointed a Committee for the purpose of investigating the practica- bility of collecting and identifying Meteoric Dust, and of considering the question of undertaking regular observations in various localities ; and that Mr. Murray be the Secretary. That Professors A. Johnson, Macgregor, J. B. Cherriman, and H. J. Bovey and Mr. C. Carpmael be reappointed a Committee for the purpose of promoting Tidal Observations in Canada ; and that Professor Johnson be the Secretary. That Professor Sylvester, Professor Cayley, and Professor Salmon be reappointed a Committee for the purpose of calculating Tables of the Fundamental Invariants of Algebraic Forms ; and that Professor Cayley be the Secretary, That Professors Everett and Sir William Thomson, Mr. G. J. Symons, Sir A. C. Ramsay, Dr. A. Geikie, Mr. J. Glaisher, Mr. Pengelly, Professor Edward Hull, Professor Prestwich, Dr. C. Le Neve Foster, Professor A. S. Herschel, Professor G. A. Lebour, Mr. A. B. Wynne, Mr. Galloway, Mr. Joseph Dickinson, Mr. G. F. Deacon, Mr. E. Wethered, and Mr. A. Strahan be reappointed a Committee for the purpose of investigating the Rate of Increase of Underground Temperature down- wards in various Localities of Dry Land and under Water ; and that Pro- fessor Everett be the Secretary. That Professor Cayley, Sir William Thomson, Mr. James Glaisher, and Mr, J. W. L. Glaisher (Secretary) be reappointed a Committee for the purpose of calculating certain tables in the Theory of Numbers connected with the divisors of a number. That Professors Tilden and Ramsay and Dr. W. W. J. Nicol be a Committee for the purpose of investigating the subject of Vapour Pressures and Refractive Indices of Salt Solutions ; and that Dr. W. W. J. Nicol be the Secretary. That Professors Ramsay, Tilden, Marshall, and W. L. Goodwin be a. Committee for the purpose of investigating certain Physical Constants of Solution, especially the expansion of saline solutions : and that Pro- fessor W. L. Goodwin be the Secretary. That Professors W. A. Tilden and H. E. Armstrong be a Committee for the purpose of investigating Isomeric Naphthalene Derivatives ; and that Professor H, E. Armstrong be the Secretary. That Professor Sir H. E. Roscoe, Mr. Lockyer, Professors Dewar, Liveing, Schuster, W. N. Hartley, and Wolcott Gibbs, Captain Abney, and Dr. Marshall Watts be a Committee for the purpose of preparing a new series of Wave-length Tables of the Spectra of the Elements ^ and that Dr. Marshall Watts be the Secretary. Ixxvi REPORT — 1885. That Professors Dewar and A. W. Williamson, Dr. Marshall Watts, Captain Abney, Dr. Johnstone Stoney, Professors W. N. Hartley, McLeod, Carey Foster, A. K. Huntington, Emerson Reynolds, Reinold, and Liveing, Lord Rayleigh, Professor Schuster, and Professor W. Chandler Roberts be a Committee for the purpose of reporting upon the present state of our knowledge of Spectrum Analysis ; and that Professor W. Chandler Roberts be the Secretary. That Professor E. Hull, Dr. H. W. Crosskey, Captain Douglas Galton, Professor J. Prestwich, and Messrs. James Glaisher, E. B. Marten, G. H. Morton, James Parker, W. Pengelly, James Plant, I. Roberts, Fox Strangways, T. S. Stooke, G. J. Symons, W. Topley, Tylden- Wright, E. Wethered, W. Whitaker, and C. E. De Ranee be reappointed a Com- mittee for the purpose of investigating the Circulation of the Under- ground Waters in the Permeable Formations of England, and the Quality and Quantity of the Waters supplied to various towns and districts from these formations ; and that Mr. De Ranee be the Secretary. That Professors J. Prestwich, W. Boyd Dawkins, T. McK. Hughes, and T. G. Bonney, Dr. H. W. Crosskey, and Messrs. C. E. De Ranee, H. G. Fordham, J. E. Lee, D. Mackintosh, W. Pengelly, J. Plant, and R. H. Tiddeman be reappointed a Committee for the purpose of record- ing the position, height above the sea, lithological characters, size, and origin of the Erratic Blocks of England, Wales, and L-eland, reporting other matters of interest connected with the same, and taking measures for their preservation ; and that Dr. Crosskey be the Secretary. That Sir A. Taylor, Professor Bayley Balfour, Dr. Crombie Brown, Dr. Cleghorn, and Sir John Lubbock be a Committee for the purpose of considering whether the condition of our Forests and Woodlands might not be improved by the establishment of a Forest School. That Sir Joseph D. Hooker, Sir George Nares, Mr. John Murray, General J. T. Walker, Admiral Sir Leopold McClintock, Dr. W. B. Carpenter, Mr. Clements Markbam, and Admiral Sir Erasmus Ommanney, be a Committee for the purpose of drawing attention to the desirability of further research in the Antarctic Regions, nearly half a century having elapsed since the last exploration; and that Admiral Sir Erasmus ■Ommanney be the Secretary. That General J. T. Walker, Sir J. H. Lefroy, Sir William Thomson, Mr. Alexander Buchan, Mr. J. Y. Buchanan, Mr. John Murray, Mr. Francis Galton, Mr. H. W. Bates, and Mr. E. G. Ravenstein, with power to add to their number, be a Committee for the purpose of taking into consideration the combination of the Ordnance and Admiralty Sur- veys, and the production of a batho-hypsographical map of the British Islands ; and that Mr. E. G. Ravenstein be the Secretary. That General J. T. Walker, Sir William Thomson, Sir J. H. Lefroy, General R. Strachey, Professor A. S. Herschel, Professor G. Chrystal, Professor C. Niven, Professor J. H. Poynting, and Professor A. Schuster be a Committee for the purpose of inviting designs for a good Differential Gravity Meter in supersession of the pendulum, whereby satisfactory results may be obtained, at each station of observation, in a few hours, instead of the many days over which it is necessary to extend pendulum observations ; and that Professor J. H. Poynting be the Secretary. That Dr. J. H. Gladstone, Professor Armstrong, Mr. William Shaen, Mr. Stephen Bourne, Miss Lydia Becker, Sir John Lubbock, Dr. H. W. Crosskey, Sir Richard Temple, Sir Henry E. Roscoe, Mr. James EECOMMENDATIONS ADOPTED BY THE GENERAL COMMITTEE. Ixxvil Hey wood, and Professor N. Story Maskelyne be reappointed a Committee for the purpose of continuing the inquiries relating to the teaching of Science in Elementary Schools ; and that Dr. J. H. Gladstone be the Secretary. That the Corresponding Societies Committee, consisting of Mr. F. Galton, Professor "Williamson, Captain Douglas Galton, Professor Boyd Dawkins, Sir Rawson Rawson, Dr. Garson, Mr. J. Evans, Mr. J. Hopkinson, Mr. Whitaker, Mr. Symons, Professor Meldola (Secretary), and General Pitt- Rivers, be reappointed. That Mr. Mollison be requested to report on the present state of our knowledge of the Mathematical Theory of Thermal Conduction. That Mr. P. T. Main be requested to draw up a Report on our experi- mental knowledge of the Properties of Matter with respect to volume,, pressure, temperature, and specific heat. That Mr. Glazebrook be requested to continue his Report on Optics. That Professor J. J. Thomson be requested to continue his Report on. Electrical Theories. Communications ordered to be printed in extenso in the Annual Seport of the Association. Mr. Meldrum's paper, ' A Tabular Statement of the dates at which,, and the localities where Pumice or Volcanic Dust was seen in the Indian Ocean ' (with one plate). Professor 0. J. Lodge's paper ' On Electrolysis,' opening the discussion on Electrolysis. , Mr. Barker's paper ' On Slaty Cleavage.' That Mr. Whitaker be requested to enlarge his List of Works on the Geology of Staffordshire by the addition of lists on Warwickshire and Worcestershire, and that the same be printed in full in the Report. Mr. Stephen Bourne's paper ' On the use of Index Numbers in the Investigation of Trade Statistics.' Mr. W. H. Preece's paper ' On the Strength of Telegraph Poles.' Mr. A. S. Biggart's paper ' On the Forth Bridge Works,' with the necessary plates. Mr. J. N. Shoolbred's paper ' On the Electric Lighting of the Forth Bridge.' Mr. C. Barlow's paper ' On the Tay Bridge,' with the necessary plates^ Resolutions referred to the Council for Consideration, and Action if desirable. That the Council be requested to reconsider the proposal of holding a General International Congress, and to report to the General Committee thereon at the next Meeting of the Association. That the Council be requested to consider the desirability of admitting ladies as Officers of the Association, or as Members of the General or Sectional Committees. That the Council be requested to consider the advisability of renderino- the special Reports of the Association more accessible to the scientific public by placing them on sale in separate form. That the printed Reports on Special Subjects be oflPered for sale to- Ixxviii EEPOUT — 1885. the general public at the time of the Meeting, or as soon afterwards as possible. That the Conncil be requested to so modify the Rules of the Associa- tion as to permit of a Sectional Meeting being held at an earlier hour than eleven, and the Sectional Committee previously, due notice being given to the Section on the previous day. That a memorial be presented to H.M. Government requesting them to enlarge the existing Agricultural Department of the Privy Conncil, with the view of concentrating all administrative functions relating to Agriculture in one fully- equipped Board and Department of Agriculture. That the Council be requested to consider and take steps, if they think it desirable, to memorialise the Government to undertake the more systematic collection and annual publication of Statistics of Wages, and a periodical industrial census. That a memorial be presented to H.M. Government in favour of the establishment of a National School of Forestry. i SYNOPSIS jOF GEANTS OF MONEY. Ixxix Synopsis of Grants of Money appropriated to Scientific Pur- poses by the General Committee at the Aberdeen Meeting in September 1885. The Names of the Members entitled to call on the General Treasurer for the respective Grants are prefixed. Mathematics and Physics. £ s. d. *Foster, Professoi- G. Carey. — Electrical Standards 40 *Stewart, Professor Balfour. — Solar Radiation 20 *Stewart, Professor Balfour. — Meteorological Observations at Chepstow 25 Darwin, Professor G. H. — Instructions for Tidal Observations 50 *Stewart, Professor Balfour. — Comparing and reducing Mag- netic Observations 40 *Forbes, Professor G. — Standards of Light , 20 *Brown, Professor Crum. — Ben Nevis Observatory 100 *Armstrong, Professor. — Physical and Chemical bearings of Electrolysis 20 diemistry. M'Leod, Professor. — Silent discharge of Electricity into at- mosphere 20 *Williamson, Professor A. W. — Chemical Nomenclature 6 Geology. *Blanford, Mr. W. T.— Fossil plants of the Tertiary and Secondary Beds 20 Hughes, Professor T. McK. — Caves of North Wales 25 *Etheridge, Mr. R. — Volcanic Phenomena in Japan 50 *Grantbam, R. B. — Erosion of Sea Coasts 20 ♦Bauerman, Mr. H. — Volcanic Phenomena of Vesuvius 30 *E vans, Dr. J. — Geological Record 100 ^Etheridge, Mr. R. — Fossil Phyllopoda 15 Carried forward ^600 * Eeappointed. IXXX KEPOET 1885, & s. d. Brought forward 600 Biology. *Stanton, Mr. H. T.— Zoological Record 100 *Mrirray, Mr. J. — Marine Biological Station at Grantham ... 75 *Lankester, Professor Ray. — Zoological Station at Naples ... 50 Cleland, Professor. — Researches in Food Fishes and Inver- tebrata at St. Andrews 75 *Cordeaux, Mr. J.— Migration of Birds 30 Cleland, Professor. — Mechanism of Secretion of Urine 10 Geography. Walker, General J. T. — New Guinea Exploration 150 0' Walker, General J. T. — Investigation into depth of perma- nently frozen soil in Polar Regions 5 0' Economic Science and Statistics. Sidgwick, Professor. — Regulation of Wages under sliding scales 10 Mechanics. Barlow, Mr. W. H. — Effect of varying stresses on metals ... 10 Anthropology. i Garson, Dr. — Investigation into a pre-historic race in the Greek Islands 20 *Tylor, Dr. E. B. — Investigation into North- Western Tribes ofCanada 50 *Galton, Mr. F. — Racial characteristics in British Isles 10 £1195 * Eeappointed. The Annual Meeting in 1886. The Meeting at Birmingham will commence on Wednesday, Sep- tember 1. Place of Meeting in 1887 . The Annual Meeting of the Association will be held at Manchester. GENERAL SXATEMEST. Ixxxi General Statement of Sums ivhich have been paid on account of Grants for Scientific Purposes. 1834. Tide Discussions 20 1835. Tide Discussions 62 British Fossil Ichthyology ■■■ 105 ±'167 1836. Tide Discussions 163 British Fossillchthyology ... 105 Thermometric Observations, &c 50 Experiments on long-con- tinued Heat 17 1 Eain-Gauges 9 13 Refraction Experiments 15 Lunar Nutation 60 Thermometers 15 6 £435 1837. Tide Discussions 284 1 Chemical Constants 24 13 6 Lunar Nutation 70 Observations on Waves 100 12 Tides at Bristol 150 Meteorology and Subterra- nean Temperature 93 3 Vitrification Experiments ... 150 Heart Experiments 8 4 6 Barometric Observations 30 Barometers 11 18 6 £922 12 6 1838. Tide Discussions 29 British Fossil Fishes 100 Meteorological Observations and Anemometer (construc- tion) 100 Cast L-on (Strength of) 60 Animal and Vegetable Sub- stances (Preservation of) ... 19 1 10 Eailway Constants 41 12 10 Bristol Tides 50 Growth of Plants 75 Mud in Rivers 3 6 6 Education Committee 50 Heart Experiments 5 3 Land and Sea Level 267 8 7 Steam-vessels 100 Meteorological Committee ... 31 9 5 £932 2 2 1839. Fossillchthyology 110 Meteorological Observations at Plymouth, &c 63 10 1885. £ s. d. Mechanism of Waves 144 2 Bristol Tides 35 18 6 Meteorology and Subterra- nean Temperature 21 11 Vitrification Experiments ... 9 4 7 Cast-Iron Experiments 103 Railway Constants 28 7 2 Land and Sea Level 274 1 4 Steam- vessels' Engines 100 Stars in Histoire Celeste 171 18 6 Stars in Lacaille 11 Stars in R.A.S. Catalogue ... 166 16 6 Animal Secretions 10 10 Steam Engines in Cornwall... 50 Atmospheric Air 16 1 Cast and Wrought Iron 40 Heat on Organic Bodies 3 Gases on Solar Spectrum 22 Hdurly Meteorological Ob- servations, Inverness and Kingussie 49 7 8 Fossil Reptiles 118 2 9 Mining Statistics 50 £1595 11 1840. Bristol Tides 100 a Subterranean Temperature ... 13 13 6 Heart Experiments 18 19 Lungs Experiments 8 13 Tide Discussions 60 Land and Sea Level 6 11 1 Stars (Histoire Celeste) 242 10 Stars (Lacaille) 4 15 Stars (Catalogue) 264 0- Atmospheric Air 15 15 Water on Iron 10 Heat on Organic Bodies 7 & Meteorological Observations . 52 17 6 Foreign Scientific Memoirs... 112 1 6 Working Population 100 School Statistics 50 Forms of Vessels 184 7 Chemical and Electrical Phe- nomena 40 Meteorological Observations at Plymouth 80 Magnetical Observations 185 13 9 £1546 16 4 1841. Observations on Waves 30 Meteorology and Subterra- nean Temperature 8 Actinometers 10 Earthquake Shocks 17 Acrid Poisons .. 6 Veins and Absorbents 3 Mud in Rivers 5 e 8 7 Ixxxii KEPORT — 1885. £ s. d. Marine Zoology 15 12 8 Skeleton Maps 20 Mountain Barometers 6 18 6 Stars (Histoire Celeste) 185 Stars (Lacaille) 79 5 Stars (Nomenclature of) 17 19 6 Stars (Catalogue of ) 40 Water on Iron 50 Meteorological Observations at Inverness 20 Meteorological Observations (reduction of ) 25 Fossil Reptiles 50 Foreign Memoirs 62 6 Railvsray Sections 38 1 Forms of Vessels 193 12 Meteorological Observations at Plymouth 55 Magnetical Observations 61 18 8 Fishes of the Old Red Sand- stone 100 Tides at Leith 50 Anemometer at Edinburgh ... 69 1 10 Tabulating Observations 9 6 3 Races of Men 5 Radiate Animals 2 £1235 10 U 18-12. Dynamometric Instruments . . 113 11 2 Anoplura Britannice 52 12 Tides at Bristol 59 8 GasesonLight 30 14 7 Chronometers 26 17 6 Marine Zoology 15 British Fossil Mammalia 100 Statistics of Education 20 Marine Steam-vessels' En- gines 28 Stars (Tlistoire Celeste) ...... 69 Stars (Brit. Assoc. Cat. of) ... 110 Railway Sections 161 10 British Belemnites .. 50 Fossil Reptiles (publication of Report) 210 Forms of Vessels 180 Galvanic Experiments on Rocks 5 8 6 Meteorological Experiments at Plymouth 68 Constant Indicator and Dyna- mometric Instruments 90 Force of Wind 10 Light on Growth of Seeds ... 8 Vital Statistics 50 Vegetative Power of Seeds ... 8 1 11 Questions on Human Race ... 7 9 £1449 17 8 1843. Revision of the Nomenclature of Stars 2 £ s. d. Reduction of Stars, British Association Catalogue 25 Anomalous Tides, Frith of Forth 120 Hourly Meteorological Obser- vations at Kingussie and Inverness 77 12 8 Meteorological Observations at Plymouth 55 Whewell's Meteorological Anemometer at Plymouth . 10 Meteorological Observations, Osier's Anemometer at Ply- mouth 20 Reduction of Meteorological Observations 30 Meteorological Instruments and Gratuities 39 6 Construction of Anemometer at Inverness 56 12 2 Magnetic Co-operation 10 8 10 Meteorological Recorder for Kew Observatory 50 Action of Gases on Light 18 16 1 Establishment at Kew Ob- servatory, Wages, Repairs Furniture, and Sundries ... 133 4 7 Experiments by Captive Bal- loons 81 8 Oxidation of the Rails of Railways 20 Publication of Report on Fossil Reptiles 40 Coloured Drawings of Rail- way Sections 147 18 3 Registration of Earthquake Shocks 30 Report on Zoological Nomen- clature 10 Uncovering Lower Red Sand- stone near Manchester 4 4 Vegetative Power of Seeds ... 5 3 Marine Testacea (Habits of) . 10 Marine Zoology 10 Marine Zoology 2 14 Preparation of Report on Bri- tish Fossil Mammalia 100 Physiological Operations of Medicinal Agents 20 Vital Statistics 36 5 8 Additional Experiments on the Forms of Vessels 70 Additional Experiments on the forms of Vessels 100 Reduction of Experiments on the Forms of Vessels 100 Morin's Instrument and Con- stant Indicator 69 14 10 Experiments on the Strength of Materials 6 8 11 ... 60 £1565 10 2 GENERAL STATEMENT. Ixsxiii £ s. d. 184i. Meteorological Observations at Kingussie and Inverness 12 Completing Observations at PljTuouth 35 Magnetic and Meteorological Co-operation 25 8 4 Publication of the British Association Catalogue of Stars 35 Observations on Tides on the East Coast of Scotland ... 100 Revision of the Nomenclature of Stars 18i2 2 9 6 Maintaining the Establish- ment in Kew Observa- tory 117 17 3 Instruments for Kew Obser- vatory ... 56 7 3 Influence of Light on Plants 10 Subterraneous Temperature in Ireland 5 Coloured Drawings of Rail- way Sections 15 17 6 Investigation of Fossil Fishes of the Lower Tertiary Strata 100 Registering the Shocks of Earthquakes 1842 23 11 10 Structure of Fossil Shells ... 20 Radiata and Mollusca of the ^gean and Red Seas 1842 100 Geographical Distributions of Marine Zoology 1842 10 Marine Zoology of Devon and Cornwall 10 Marine Zoology of Corfu 10 Experiments on the Vitality of Seeds 9 Experiments on the Vitality of Seeds 1842 8 7 3 Exotic Anoplura 15 Strength of Materials 100 Completing Experiments on the Forms of Ships 100 Inquiries into Asphyxia 10 Investigations on the Internal Constitution of Metals 50 Constant Indicator and Mo- rin's Instrument 1842 10 ■ £981 12 "8 1845. Publication of the British As- sociation Catalogue of Stars 351 14 6 Meteorological Observations at Inverness 30 IS 11 Jlagnetic and Meteorological Co-operation 16 16 8 Meteorological Instruments at Edinburgh 18 11 9 Reduction of Anemometrical Observations at Plymouth 25 £ s. d. Electrical Experiments at Kew Observatory 43 17 8 Maintaining the Establish- ment in Kew Observatory 149 For Kreil's Barometrograph 25 Gases from Iron Furnaces... 50 The Actinograph 15 Microscopic Structure of Shells 20 Exotic Anoplura 1843 10 Vitality of Seeds 1843 2 Vitality of Seeds 1844 7 Marine Zoology of Cornwall 10 Physiological Action of Medi- cines 20 Statistics of Sickness and Mortality in York 20 Earthquake Shocks 18 43 15 14 8 £831 9~~9 15 7 1847. Computation of the Gaussian Constants for 1829 50 Habits of Marine Animals ... 10 Physiological Action of Medi- cines 20 Blarine Zoology of Cornwall 10 Atmospheric Waves 6 Vitality of Seeds 4 Maintaining the Establish- ment at Kew Observatory 107 £208 1846. British Association Catalogue of Stars 1844 211 15 Fossil Fishes of the London Clay 100 Computation of the Gaussian Constants for 1829 50 Maintaining the Establish- ment at Kew Observatory 146 Strength of Materials 60 Researches in Asphyxia 6 Examination of Fossil Shells 10 Vitality of Seeds 1 844 2 Vitality of Seeds 1845 7 Marine Zoology of Cornwall 10 Marine Zoology of Britain ... 10 Exotic Anoplura 1814 25 Expenses attending Anemo- meters 11 Anemometers' Repairs 2 Atmospheric Waves 3 Captive Balloons 1844 8 Varieties of the Human Race 1844 7 6 3 Statistics of Sickness and Mortality in York 12 £685 16 16 7 16 2 15 10 12 3 7 6 3 6 3 3 19 8 9 3 7 7 8 6 5 4 62 Ixxxiv KEPORT — 1885. £ s. d. 1848. Maintainingr the Establish- ment at Kew Observatory 171 15 11 Atmospheric Waves 3 10 9 Vitality of Seeds 9 15 Completion of Catalogue of Stars 70 On Colouring Matters 5 On Growth of Plants •• 15 £275 1 8 1819. Electrical Observations at Kew Observatory 50 Maintaining the Establish- ment at ditto 76 2 5 Vitality of Seeds 5 8 1 On Growth of Plants 5 Kegistration of Periodical Phenomena 10 Bill on Account of Anemo- metrical Observations 1 3 9 £169 19 6 1850. Maintaining the Establish- ment at Kew Observatory 255 18 Transit of Earthquake "Waves 50 Periodical Phenomena 15 Meteorological Instruments, Azores 25 £345 18 1851 Maintaining the Establish- ment at Kew Observatory (includes part of grant in 1849) 309 2 2 Theory of Heat 20 1 1 Periodical Phenomena of Ani- mals and Plants 5 Vitality of Seeds 5 6 4 Influence of Solar Kadiation 30 Ethnological Inquiries 12 Researches on Annelida 10 £391 9~7 1852. Maintaining the Establish- ment at Kew Observatory (including balance of grant for 1850)... 233 17 8 Experiments on the Conduc- tion of Heat 5 2 9 Influence of Solar Radiations 20 Geological Map of Ireland ... 15 Researches on the British An- nelida 10 Vitality of Seeds 10 6 2 Strength of Boiler Plates 10 £304 6 7 £ ». d. 1853. Maintaining the Establish- ment at Kew Observatory 165 Experiments on the Influence of Solar Radiation 15 Researches on the British Annelida 10 Dredging on the East Coast of Scotland 10 Ethnological Queries ^^ 5_ £205 a 1854. Maintaining the Establish- ment at Kew Observatory (including balance of former grant) 330 15 4 Investigations on Flax 11 Effects of Temperature on Wrought Iron 10 Registration of Periodical Phenomena 10 British Annelida 10 Vitality of Seeds 5 2 3 Conduction of Heat 4 2 £380 19 7 18.55. Maintaining the Establish- ment at Kew Observatory 425 Earthquake Movements 10 Physical Aspect of the Moon 118 5 Vitality of Seeds 10 7 11 Map of the World 15 Ethnological Queries 5 Dredging near Belfast .^ 4 £480T6~^ 575 1856. Maintaining the Establish- ment at Kew Observa- tory:— 1854 £ 75 0\ 1855 £500 0/ Strickland's Ornithological Synonyms 100 Dredging and Dredging Forms 9 13 Chemical Action of Light ... 20 Or Strength of Iron Plates 10 Registration of Periodical Phenomena 10 Propagation of Salmon 10 £734 13 9- 1857. Maintaining the Establish- ment at Kew Observatory 350 Earthquake Wave Experi- ments 40 Dredging near Belfast 10 O' Dredging on the West Coast of Scotland 10 a GENERAL STATEMENT. Ixxxv 5 7 4 ... 5 £507 15 4 £ s. d. Investigations into the Mol- lusca of California 10 Experiments on Flax 5 Natural History of Mada- gascar 20 Researches on British Anne- lida 25 Eeport on Natural Products imported into Liverpool ... 10 Artificial Propagation of Sal- mon 10 Temperature of Mines 7 8 Thermometers for Subterra- nean Observations Life-boats 18.58. Maintaining the Establish- ment at Kew Observatory 500 Earthquake Wave Experi- ments 25 Dredging on the West Coast of Scotland 10 Dredging near Dublin 5 Vitality of Seeds 5 5 Dredging near Belfast 18 13 2 Report on the British Anne- lida 25 Experiments on the produc- tion of Heat by Motion in Fluids 20 Report on the Natural Pro- ducts imported into Scot- land 10 £618 18 2 1859. Maintaining the Establish- ment at Kew Observatory 500 Dredging near Dublin 15 Osteology of Birds 50 Irish Tunicata 5 Manure Experiments 20 British Medusidas 5 Dredging Committee 5 Steam-vessels' Performance... 5 Marine Fauna of South and AVest of Ireland 10 Photographic Chemistry 10 Lanarljshire Fossils 20 1 Balloon Ascents 39 11 £684 11 1 1860. Maintaining the Establish- ment at Kew Observatory 500 Dredging near Belfast 16 6 Dredging in Dublin Bay 15 Inquiry into the Performance of Steam-vessels ]24 Explorations in the Yellow Sandstone of Dura Don ... 20 Chemico-mechanical Analysis of Rocks and Minerals 25 Researches on the Growth of Plants 10 Researches on the Solubility of Salts 30 Researches on the Constituents of Manures 25 Balance of Captive Balloon Accounts 1 ». d, 13 6 £766 19 6 1861. Maintaining the Establish- ment of Kew Observatory.. 500 Earthquake Experiments 25 Dredging North and East Coasts of Scotland 23 Dredging Committee : — 1860 £50 \ 1861 £22 0/ Excavations at Dura Den 20 Solubility of Salts 20 Steam- vessel Performance ... 150 Fossils of Lesmahago 15 Explorations at Uriconium... 20 Chemical Alloys 20 Classified Index to the Trans- actions 100 Dredging in the Mersey and Dee 5 Dip Circle 30 Photoheliographic Observa- tions 50 Prison Diet 20 Gauging of Water 10 Alpine Ascents 6 Constituents of Manures 25 72 5 10 £1111 5 10 1862. Maintaining the Establish- ment of Kew Observatory 500 Patent Laws 21 Mollusca of N.- W. of America 10 Natural History by Mercantile Marine 5 Tidal Observations 25 Photoheliometer at Kew 40 Photographic Pictures of the Sun 150 Rocks of Donegal 25 Dredging Durham and North- umberland 25 Connexion of Storms 20 Dredging North-east Coast of Scotland 6 Ravages of Teredo 3 Standards of Electrical Re- sistance 50 Railway Accidents 10 Balloon Committee 200 Dredging Dublin Bay 10 6 9 6 11 Jxxxvi repout — 1885. £ s. d. Dredging the Mersey 5 Prison Diet 20 Gauging of Water 12 10 Steamships' Performance 150 Thermo- Electric Currents 5 £1293 16 6 18C3. Maintaining the Establish- ment of Kew Observatory.. 600 Balloon Committee deficiency 70 Balloon Ascents (other ex- penses) 25 Entozoa 25 Coal Fossils 20 Herrings 20 Granites of Donegal 5 Prison Diet 20 Vertical Atmospheric Move- ments 13 Dredging Shetland 50 Dredging North-east coast of Scotland 25 Dredging Northumberland and Durham 17 Dredging Committee superin- tendence 10 Steamship Performance 100 Balloon Committee 200 Carbon under pressure 10 Volcanic Temperature 100 Bromide of Ammonium 8 Electrical Standards 100 Electrical Construction and- Distribution 40 Luminous Meteors 17 Kew Additional Buildings for Photoheliograph 100 Thermo-EIectricity 15 Analysis of Eocks 8 Hydroida 10 £1608 3 10 3 10 1864. Maintaining tlie Establish- ment of Kew Observatory.. 600 Coal Fossils 20 Vertical Atmospheric Move- ments 20 Dredging Shetland 75 Dredging Northumberland... 25 Balloon Committee 200 Carbon under pressure 10 Standards of Electric Ke- sistance 100 Analysis of Piocks 10 Hydroida 10 Askham's Gift 50 Nitrite of Amyle 10 Nomenclature Committee ... 5 Eain-Gauges 19 15 8 Cast-iron Investigation 20 £ s. d Tidal Observations in the Humber 50 Spectral Kays 45 Luminous Meteors 20 £1289 15 8 1865. — — — — Maintaining the Establish- ment of kew Observatory.. 600 Balloon Committee 100 Hydroida 13 Eain-Gauges 30 Tidal Observations in the Humber 6 8 Hexylic Compoimds 20 Amyl Compounds 20 Irish Flora 25 American Mollusca 3 9 Organic Acids 20 Lingula Flags Excavation ... 10 Eurj^Dterus 50 Electrical Standards 100 Malta Caves Eesearches 30 Oyster Breeding 25 Gibraltar Caves Eesearches... 150 Kent's Hole Excavations 100 Moon's Surface Observations 35 Marine Fauna 25 Dredging Aberdeenshire 25 Dredging Channel Islands ... 50 Zoological Nomenclature 5 Eesistance of Floating Bodies inAVater 100 Bath Waters Analysis 8 10 10 Luminous Meteors 40 £1591 7 10 1866. Maintaining the Establish- ment of Kew Observatory. . 600 Lunar Committee 64 13 4 Balloon Committee 50 Metrical Committee 60 British Eainfall 50 Kilkenny Coal Fields 16 Alum Bay Fossil Leaf-Bed ... 15 Luminous Meteors 50 Lingula Flags Excavation ... 20 Chemical Constitution of Cast Iron 60 Amyl Compotinds 25 Electrical Standards 100 Malta Caves Exijloration 30 Kent's Hole Exploration 200 Marine Fauna, &c., Devon and Cornwall 25 Dredging Aberdeenshire Coast 25 Dredging Hebrides Coast ... 60 Dredging the Mersey 5 Eesistance of Floating Bodies in Water 60 Polycyanidesof Organic Eadi- cals 29 GENERAL STATEMENT. Ixxxvii £ s. d. Riffor Mortis 10 Irish Annelida 15 Catalogue of Crania 50 Didine Birds of Mascarene Islands 50 Tj'pical Crania Researches ... 30 Palestine Exploration Fun d... 100 :gl750 13 4 1867. Maintaining the Establish- ment of Kew Observatory.. 600 Meteorological Instruments, Palestine..... 50 Lunar Committee 120 Metrical Committee 30 Kent's Hole Explorations ... 100 Palestine Explorations 50 Insect Fauna, Palestine 30 British Rainfall 50 Kilkenny Coal Fields 25 Alum Bay Fossil Leaf -Bed ... 25 Luminous Meteors 50 Bournemouth, &c., Leaf-Beds 30 Dredging Shetland 75 Steamship Reports Condensa- tion 100 Electrical Standards 100 Ethyl and Methyl series 25 Fossil Crustacea 25 Sound under Water 24 4 North Greenland Fauna 75 Do. Plant Beds 100 Iron and Steel Manufacture... 25 Patent Laws 30 £1739 4 1868. Maintaining the Establish- ment of Kew Observatory. . 600 Lunar Committee 120 Metrical Committee 50 Zoological Record 100 Kent's Hole Explorations ... 150 Steamship Performances 100 British Rainfall 50 Luminous Meteors 50 Organic Acids 60 Fossil Crustacea 25 Methyl Series 25 Mercury and Bile 25 Organic Remains in Lime- stone Rocks 25 Scottish Earthquakes 20 Fauna, Devon and Cornwall.. 30 British Fossil Corals 50 Bagshot Leaf-Beds 50 Greenland Explorations 100 Fossil Flora : 25 Tidal Observations 100 Underground Temperature ... 50 Spectroscopic Investigations of Animal Substances 5 Secondary Reptiles, &c 30 British Marine Invertebrate Fauna -. 100 £1'J40 1869. *^^^ Maintaining the Establish- ment of Kew Observatory. . 600 Lunar Committee 50 Metrical Committee 25 Zoological Record 100 Committee on Gases in Deep- well Water 25 British Rainfall 50 Thermal Conductivity of Iron, &c 30 Kent's Hole Explorations 150 Steamship Performances 30 Chemical Constitution of Cast Iron 80 Iron and Steel Manufacture 100 Methyl Series 30 Organic Remains in Lime- stone Rocks 10 Earthquakes in Scotland 10 British Fossil Corals 50 Bagshot Leaf-Beds 30 Fossil Flora 25 Tidal Observations 100 Underground Temperature ... 30 Spectroscopic Investigations of Animal Substances 5 Organic Acids 12 Kiltorcan Fossils 20 Chemical Constitution and Physiological Action Rela- tions 15 Mountain Limestone Fossils 25 Utilization of Sewage 10 Products of Digestion 10 £1622' 1870. Maintaining the Establish- ment of Kew Observatory 600 Metrical Committee 25 Zoological Record 100 Committee on Marine Fauna 20 Ears in Fishes 10 Chemical Nature of Cast Iron 80 Luminous Meteors 30 Heat in the Blood 15 British Rainfall 100 Thermal Conductivity of Iron, &c : 20 British Fossil Corals 50 Kent's Hole Explorations ... 150 Scottish Earthquakes 4 Bagshot Leaf- Beds 15 Fossil Flora 25 Tidal Observations 100 Underground Temperature ... 50 Kiltorcan Quarries Fossils ... 20 «. d. Ixxxviii EEPORT — 1885. £ Mountain Limestone Fossils 25 Utilization of Sewage 50 Organic Chemical Compounds 30 Onny River Sediment 3 Mechanical Equivalent of Heat ••• 50 £1572 J871. Maintaining the Establish- ment of Kew Observatory 600 Monthly Reports of Progi'ess in Chemistry 100 Metrical Committee 25 Zoological Record 100 Thermal Equivalents of the Oxides of Chlorine 10 Tidal Observations 100 Fossil Flora 25 Luminoiis Meteors 30 British Fossil Corals 25 Heat in the Blood 7 British Rainfall 50 Kent's Hole Explorations ... 150 Fossil Crustacea 25 Methyl Compounds 25 Lunar Objects 20 Fossil Coral Sections, for Photographing 20 Bagshot Leaf-Beds 20 Moab Explorations 100 Gaussian Constants 40 £1472 1872. Maintaining the Establish- ment of Kew Observatory 300 Metrical Committee 75 Zoological Record 100 Tidal Committee 200 Carboniferous Corals 25 Organic Chemical Compounds 25 Exploration of Moab 100 Terato-Embryological Inqui- ries 10 Kent's Cavern Exploration.. 100 Luminous Meteors 20 Heat in the Blood 15 Fossil Crustacea 25 Fossil Elephants of Malta ... 25 Lunar Objects 20 Inverse Wave-Lengths 20 British Rainfall 100 Poisonous Substances Antago- nism 10 Essential Oils, Chemical Con- stitution, &c 40 Mathematical Tables 50 Thermal Conductivity of Me- tals s. d. 2 6 2 6 .... 25 £1285 £ s. d. 1873. Zoological Record 100 Chemistry Record 200 Tidal Committee 400 Sewage Committee 100 Kent's Cavern Exploration ... 150 Carboniferous Corals 25 Fossil Elephants 25 Wave-Lengths 150 British Rainfall 100 Essential Oils 30 Mathematical Tables 100 Gaussian Constants •.... 10 Sub-Wealden Explorations... 25 Underground Temperature ... 150 Settle Cave Exploration 50 Fossil Flora, Ireland 20 Timber Denudation and Rain- fall 20 Luminous Meteors .'^O £1685 1874. "* ■ Zoological Record 100 Chemistry Record 100 Mathematical Tables 100 Elliptic Functions 100 Lightning Conductors 10 Thermal Conductivity of Rocks 10 Anthropological Instructions, &c 50 Kent's Cavern Exploration... 150 Luminous Meteors 30 Intestinal Secretions 15 British Rainfall 100 Essential Oils 10 Sub-Wealden Explorations... 25 Settle Cave Exploration 50 Mauritius Meteorological Re- search 100 Magnetization of Iron 20 Marine Organisms 30 Fossils, North- West of Scot- land 2 10 Physiological Action of Light 20 Trades Unions 25 Mountain Limestone-Corals 25 Erratic Blocks 10 Dredging, Durham and York- shire Coasts 28 5 High Temperature of Bodies 30 Siemens 's Pyrometer 3 6 Labyrinthodonts of Coal- Measures 7 15 £1151 16 1875. Elliptic Functions 100 Magnetization of Iron 20 British Rainfall 120 Luminous Meteors 30 Chemistry Record 100 GENERAL STATEMENT. Ixxxix £ s. d. Specific Volume of Liquids... 25 Estimation of Potash and Phosphoric Acid 10 Isometric Cresols 20 Sub- Wealden Explorations... 100 Kent's Cavern Exploration... 100 Settle Cave Exploration 50 Earthquakes in Scotland 15 Underground Waters 10 Development of Myxinoid Fishes 20 Zoological Record 100 Instructions for Travellers ... 20 Intestinal Secretions 20 Palestine Exploration 100 £960 1876. Printing Mathematical Tables 159 4 2 British Rainfall 100 Ohm's Law 9 15 Tide Calculating Machine ... 200 Specific Volume of Liquids... 25 Isomeric Cresols 10 Action of Ethyl Bromobuty- rate on Ethyl Sodaceto- acetate 5 Estimation of Potash and Phosphoric Acid 13 Exploration of Victoria Cave, Settle 100 Geological Record 100 Kent's Cavern Exploration... 100 Thermal Conductivities of Rocks 10 Underground Waters 10 Earthquakes in Scotland 1 10 Zoological Record 100 Close Time 5 Physiological Action of Sound 25 Zoological Station 75 Intestinal Secretions 15 Physical Characters of Inha- bitants of British Isles 13 15 Measuring Speed of Ships ... 10 Effect of Propeller on turning of Steam Vessels 5 £1092 4 2 1877. Liquid Carbonic Acids in Minerals 20 Elliptic Functions 250 Thermal Conductivity of Rocks 9 11 7 Zoological Record 100 Kent's Cavern 100 Zoological Station at Naples 75 Luminous Aleteors 30 Elasticity of Wires 100 Dipterocarpse, Report on 20 £ «. d. Mechanical Equivalent of Heat 35 Double Compounds of Cobalt and Nickel 8 Underground Temperatures 50 Settle Cave Exploration 100 Underground Waters in New Red Sandstone 10 Action of Ethyl Bromobuty- rate on Ethyl Sodaceto- acetate 10 British Earthworks 25 Atmospheric Elasticity in India 15 Development of Light from Coal-gas 20 Estimation of Potash and Phosphoric Acid 1 18 Geological Record 100 Anthropometric Committee 34 Physiological Action of Phos- phoric Acid, &c 15 £1128 9 7 1878. Exploration of Settle Caves 100 Geological Record 100 Investigation of Pulse Pheno- mena by means of Syphon Recorder 10 Zoological Station at Naples 75 Investigation of Underground Waters 15 Transmission of Electrical Impulses through Nerve Structure 30 Calculation of Factor Table of Fourth Million 100 Anthropometric Committee... 66 Chemical Composition and Structure of less known Alkaloids 25 Exploration of Kent's Cavern 50 Zoological Record 100 Fermanagh Caves Exploration 15 Thermal Conductivity of Rocks 4 16 6 Luminous Meteors 10 Ancient Earthworks 25 £725 16 6 1879. Table at the Zoological Station, Naples 75 Miocene Flora of the Basalt of the North of Ireland ... 20 Illustrations for a Monograph on the Mammoth 17 Record of Zoological Litera- ture 100 Composition and Structure of less-known Alkaloids ^ - 25 xc REPORT — 1 885. £ s. d. Exploration of Caves in Borneo 50 Kent's Cavern Exploration... 100 Kecord of the Progress of Geology 100 Fermanagh Caves Exploration 5 Electrolysis of Metallic Solu- tions and Solutions of Compound Salts 25 Anthropometric Committee... 50 Natural History of Socotra... 100 Calculation of Factor Tables for 5th and 6th Millions ... 150 Circulation of Underground Waters 10 Steering of Screw Steamers... 10 Improvements in Astrono- mical Clocks 30 Marine Zoology of South Devon 20 Determination of Mechanical Equivalent of Heat 12 15 6 Specific Inductive Capacity of Sprengel Vacuum 40 Tables of Sun-heat Co- efficients 30 Datum Level of the Ordnance Survey 10 Tables of Fundamental In- variants of Algebraic Forms 36 14 9 AtmosiDheric Electricity Ob- servations in Madeira 15 Instrument for Detecting Fire-damp in Mines 22 Instruments for Measuring the Speed of Ships 17 1 8 Tidal Observations in the English Channel 10 £1 080 11 11 1880. New Form of High Insulation Key 10 Underground Temperature ... 10 Determination of the Me- chanical Equivalent of Heat 8 6 Elasticity of Wires 50 Luminous Meteors 30 Lunar Disturbance of Gravity 30 Fundamental Invariants 8 5 Laws of Water Friction 20 Sj)ecific Inductive Capacity of Sprengel Vacuum 20 Comp)letion of Tables of Sun- heat Coefficients 50 Instrument for Detection of Fire-damp in Mines 10 Inductive Capacity of Crystals and Paraffines 4 17 7 Report on Carboniferous Polyzoa 10 £ s. d. Caves of South Ireland 10 Viviparous Nature of Ichthyo- saurus 10 Kent's Cavern Exploration... 60 Geological Record 100 l\Iiocene Flora of the Basalt of North Ireland 15 Underground Waters of Per- mian Formations 5 Record of Zoological Litera- ture 100 Table at Zoological Station at Naples 76 Investigation of the Geology and Zoology of Mexico 50 Anthropometry 50 Patent Laws 5 £731 7 7 1881. Lunar Disturbance of Gravity 30 Underground Temperature ... 20 High Insulation Key 5 Tidal Observations 10 Fossil Polyzoa 10 Underground Waters 10 Earthquakes in Japan 25 Tertiary Flora 20 Scottish Zoological Station ... 50 Naples Zoological Station ... 75 Natural History of Socotra ... 50 Zoological Record 100 Weights and Heights of Human Beings 30 Electrical Standards 25 Anthropological Notes and Queries 9 Specific Refractions 7 £476 1882. Tertiarj' Flora of North of Ireland 20 Exploration of Caves of South of Ireland 10 Fossil Plants of Halifax 15 Fundamental Invariants of Algebraical Forms 76 Record of Zoological Litera- ture 100 British Polyzoa 10 Naples Zoological Station ... 80 Natural History of Timor- laut 100 Conversion of Sedimentary Materials into Metamorphic Rocks 10 Natural History of Socotra... 100 Circulation of Underground Waters 15 Migration of Birds 15 Earthquake Phenomena of Japan 25 3 1 3 1 1 11 GENERAL STATEMENT. XCl & Geological Map of Europe ... 25 Elimination of Nitrogen by Bodily Exercise 50 Anthropometric Committee... 50 Photograpliing Ultra- Violet Spark Spectra 25 Exploration of Kaygill Fis- sure 20 Calibration of Mercurial Ther- mometers 20 Wave-length Tables of Spec- tra of Elements 50 Geological Eecord 100 Standards for Electrical Measurements 100 Exploration of Central Africa 100 Albuminoid Substances of Serum 10 £1126 1883. Natural History of Timor-laut 50 British Fossil iPolyzoa 10 Circulation of Underground Waters 15 Zoological Literature Eecord 100 Exploration of Mount Kili- ma-njaro 500 Erosion of Sea-coast of Eng- land and Wales 10 Fossil Plants of Halifax 20 Elimination of Nitrogen by Bodily Exercise 38 Isomeric Naphthalene Deri- vatives 15 Zoological Station at Naples 80 Investigation of Loughton Camp 10 Earthquake Phenomena of Japan 50 Meteorological Observations on Ben Nevis 50 Fossil Phyllopoda of Palaeo- zoic Eocks 25 Migration of Birds 20 Geological Eecord 50 Exploration of Caves in South of Ireland 10 Scottish Zoological Station... 25 Screw Gauges 5 £1083~ 1884. Zoological Literature Eecord 100 Fossil Polyzoa 10 Exploration of Mount Kili- ma-njaro, East Africa 500 Anthropometric Committee... 10 Fossil Plants of Halifax 15 International Geological Map 20 Erratic Blocks of England ... 10 Natural History of Timor-laut 50 s. d. 1 11 3 3 3 3 £ s. d. Coagulation of Blood 100 Naples Zoological Station ... 80 Bibliography of Groups of Invertebrata 50 Earthquake Phenomena of Japan 75 Fossil Phyllopoda of Paleo- zoic Eocks 15 Meteorological Observatory at Chepstow 25 Migration of Birds 20 Collecting and Investigating Meteoric Dust 20 Circulation of Underground Waters 5 Ultra- Violet Spark Spectra ... 8 4 Tidal Observations 10 Meteorological Observations on Ben Nevis 50 £1173 4 1885. Zoological Literature Eecord. 100 Vapour Pressures, &c., of Salt Solutions 25 Physical Constants of Solu- tions 20 Eecent Polyzoa 10 Naples Zoological Station ... 100 Exploration of Mount Kilima- njaro 25 Fossil Plants of British Ter- tiary and Secondary Beds . 50 Calculating Tables in Theory of Numbers 100 Exploration of New Guinea... 200 Exploration of Mount Eo- raima 100 Meteorological Observations on Ben Nevis 50 Volcanic Phenomena of Vesu- vius 25 Biological Stations on Coasts of United Kingdom 150 Meteoric Dust 70 Marine Biological Station at Granton loo Fossil Phyllopoda of Palajozoic Eocks 25 Migration of Birds 30 Synoptic Chart of Indian Ocean 50 Circulation of Underground Waters 10 Geological Eecord 50 Eeduction of Tidal Observa- tions 10 Earthquake Phenomena of Japan 70 Eaygill Fissure 15 £1385 6 XCii BEPOET — 1885. General Meetings. On Wednesday, September 9, at 8 p.m., in tlie Music Hall, the Right Hon. Lord Rayleigh, M.A., D.C.L., LL.D., F.R.S., F.R.A.S., F.R.G.S., resigned the office of President to the Right Hon. Sir Lyon Playfair, K.C.B., M.P., Ph.D., LL.D., F.R.S. L. & B., F.C.S., who took the Chair, and delivered an Address, for which see page 1. On Thursday, September 10, at 8 p.m., a Soiree took place in the Art Gallery. On Friday, September 11, at 8 p.m., in the Music Hall, Professor W. G. Adams, M.A., F.R.S., F.G.S., delivered a Discourse on ' The Electric Light and Atmospheric Absorption.' On Monday, September 14, at 8.30 p.m., in the Music Hall, Mr. John Murray, F.R.S.E., delivered a Discourse on ' The Great Ocean Basins.' On Tuesday, September 15, at 8 p.m., a Soiree took place in the Art Gallery. On Wednesday, September 16, at 2.30 p.m., the concluding General Meeting took place in St. Katherine's Hall, when the Proceedings of the General Committee and the Grants of Money for Scientific purposes were explained to the Members. The Meeting was then adjourned to Birmingham. [The Meeting is appointed to commence on Wednesday, September 1, 1886.] PEE SIDE NT'S ADDEESS. 1885. ADDEESS BY THE EIGHT HOX. SHI LYON PLAYFAIE, K.C.B., M.P., F.R.S. PRESIDENT. I. Visit to Canada. OuE meeting at Montreal was a notable event in the life of the Brit- ish Association, and even marked a distinct epoch in the histoiy of civilisation. It was by no mere accident that the constitntion of the Association enabled it to embrace all parts of the British Empire. Science is truly catholic, and is bounded only by the universe. lu relation to our vast empire, science, as well as literature and art, is the common possession of all its varying people. The United Kingdom is limited to 120,800 square miles, inhabited by 35 millions of people ; but the empire as a whole has 8^ millions of square miles, with a population of 305 millions. To federate such vast possessions and so teeming a population into a political unit is a work only to be accomplished by the labours and persistent efforts of perhaps several generations of statesmen. The federation of its science is a subject of less dimensions well within the range of experi- ment. No part of the British Empire was more suited than Canada to try whether her science could be federated with our science. Canada has lately federated distinct provinces, with conflicting interests arising from difference of races, nationalities, and religions. PoHtical federation is not new in the history of the world, though it generally arises as a consequence of war. It was war that taught the Netherlands to federate in 1619. It was war which united the States in America ; federated Switzerland, Germany, and Austria, and unified Italy. But Canada formed a great national life out of petty provincial existences in a time of profound peace. This evolution gave an immense impulse to her national resources. The Dominion still requires consolidation in its vast extent, and applied science is rapidly effecting it. Canada, with its great expanse of territory, nearly as large as the United States, is being knit b2 4 REroTiT — 1885. together by the iron bands of railways from the Gulf of St. Lawrence to the Pacific Ocean, so that the fertile lands of Ontario, Manitoba, Columbia, and the North-TVestern Territories will soon be available to the world. Still practical science has much to accomplish. England and France, with only one-fifth the fertile area of Canada, support 80 millions of people, while Canada has a population not exceeding 5 millions. A less far-seeing people than the Canadians might have invited the applied science which they so much require. But they knew that with- out science there are no applications. They no doubt felt with Emerson — And what if Trade sow cities Like shells along the shore, And thatch with towns the prairie broad With railwaj's ironed o'er ; The}' are but sailing foam-bells Along Thought's causing stream. And take their shape and sun-colour From liim that sends the dream. So it was with a far-reaching foresight that the Canadian Government invited the British Association for the Advancement of Science to meet in Montreal. The inhabitants of Canada received us with open arms, and the science of the Dominion and that of the United Kingdom were welded. We found in Canada, as we had every reason to expect, men of manly and self-reliant character who loved not less than we did the old home from which they had come. Among them is the same healthi- ness of political and moral life, with the same love of truth which dis- tinguishes the English people. Our great men are their great men ; our Shakspcare, Milton, and Burns belong to them as much as to ourselves ; our Newton, Dalton, Faraday, and Darwin are their men of science as much as they are ours. Thus a common possession and mutual sympathy made the meeting in Canada a successful effort to stimulate the progress of science, while it established, at the same time, the principle that all people of British origin — and I would fain include our cousins in the United States — possess a common interest in the intellectual glories of their race, and ought, in science at least, to constitute part and parcel of a common empire, whose heart may beat in the small islands of the Northern seas, but whose blood circulates in all her limbs, carrying warmth to them and bringing back vigour to us. Nothing can be more cheering to our Association than to know that many of the young com- munities of English-speaking people all over the globe — in India, China, Japan, the Straits, Ceylon, Australia, New Zealand, the Cape — have founded scientific societies in order to promote the growth of scientific research. No doubt science, which is only a form of truth, is one in all lands, but still its unity of purpose and fulfilment received an important practical expression by our visit to Canada. This community of science will be continued by the fact that we have invited Sir William Dawson, . of Montreal, to be our next President at Birmingham, ADDRESS. O II. Science and the State. I cannot address you in Aberdeen without recollecting that when we last met in this city our President was a great prince. The just verdict of time is that, high as was his royal rank, he has a far nobler claim to our regard as a lover of humanity in its widest sense, and especially as a lover of those arts and sciences which do so much to adorn it. On September 14, 1859, I sat on this platform and listened to the eloquent address and wise counsel of the Prince Consort. At one time a member of his household, it was my privilege to co-operate with this illustrious prince in many questions relating to the advancement of science. I naturally, therefore, turned to his presidential address to see whether I might not now continue those counsels which he then gave with all the breadth and comprehensiveness of his masterly speeches. I found, as I expected, a text for my own discourse in some pregnant remarks which he made upon the relation of Science to the State. They are as follows : — 'We may be justified in hoping . . . that the Legislature and the State will more and more recognise the claims of science to their attention, so that it may no longer require the begging-box, but speak to the State like a favoured child to its parent, sure of his paternal solicitude for its welfare ; that the State will recognise in science one of its elements of strength and prosperity, to foster which the clearest dictates of self- interest demand.' This opinion, in its broadest sense, means that the relations of science to the State should be made more intimate because the advance of science is needful to the public weal. The importance of promoting science as a duty of statecraft was well enough known to the ancients, especially to the Greeks and Arabs, but it ceased to be recognised in the dark ages, and was lost to sight during the revival of letters in the fifteenth and sixteenth centuries. Germany and France, which are now in such active competition in promoting science, have only publicly acknowledged its national importance in recent times. Even in the last century, though France had its Lavoisier and Germany its Leibnitz, their Governments did not know the value of science. When the former was condemned to deatli in the Reign of Terror, a petition was presented to the rulers that his life might be spared for a few weeks in order that he might complete some important experiments, but the reply was, ' The Republic has no need of savants.' Earlier in the century the much-praised Frederick William of Prussia shouted with a loud voice, during a graduation ceremony in the University of Frankfort, ' An ounce of mother-wit is worth a ton of university wisdom.' Both France and Germany are now ashamed of these utterances of their rulers, and make energetic eflbrts to advance science with the aid of their national resources. More remarkable is it to see a young nation like the United States reserv- ing large tracts of its national lands for the promotion of scientific education. In some respects this young country is in advance of all 4 REPORT — 1885. together by the iron bands of railways from the Gulf of St. Lawrence to the PaciGc Ocean, so that the fertile lands of Ontario, Manitoba, Columbia, and the North- Western Territories will soon be available to the world. Still practical science has much to accomplish. England and France, with only one-fifth the fertile area of Canada, support 80 millions of people, while Canada has a population not exceeding 5 millions. A less far-seeing people than the Canadians might have invited the applied science which they so much require. But they knew that with- out science there are no applications. They no doubt felt with Emerson — And what if Trade sow cities Like shells along the shore, And thatch with towns the prairie broad M'ith railways ironed o'er ; They are but sailing foam-bells Along Thought's causing stream, And take their shape and sun-colour Yiom him that sends the dream. So it was with a far-reaching foresight that the Canadian Government invited the British Association for the Advancement of Science to meet in Montreal. The inhabitants of Canada received us with open arms, and the science of the Dominion and that of the United Kingdom were welded. We found in Canada, as Ave had every reason to expect, men of manly and self-reliant character who loved not less than we did the old home from whicli they had come. Among them is the same healthi- ness of political and moral life, with the same love of truth which dis- tinguishes the English people. Our great men are their great men ; our Shakspcare, !Milton, and Burns belong to them as much as to ourselves ; our Newton, Dalton, Faraday, and Darwin are their men of science as much as they are ours. Thus a common possession and mutual sympathy made the meeting in Canada a successful effort to stimulate the progress of science, while it established, at the same time, the principle that all people of British origin — and I would fain include our cousins in the United States — possess a common interest in the intellectual glories of their race, and ought, in science at least, to constitute part and parcel of a common empire, whose heart may beat in the small islands of the Northern seas, but whose blood circulates in all her limbs, carrying warmth to them and bringing back vigour to us. Nothing can be more cheering to our Association than to know that many of the young com- munities of English-speaking people all over the globe — in India, China, Japan, the Straits, Ceylon, Australia, New Zealand, the Cape — have founded scientific societies in order to promote the growth of scientific research. No doubt science, which is only a form of truth, is one in all lands, but still its unity of purpose and fulfilment received an important practical expression by our visit to Canada. This community of science will be continued by the fact that we have invited Sir William Dawson, of Montreal, to be our next President at Birmingham. ADDRESS. O II. Science and the State. 1 cannot address you in Aberdeen without recollecting that when we last met in this city our President was a great prince. The just verdict of time is that, high as was his royal i-ank, he has a far nobler claim to our regard as a lover of humanity in its widest sense, and especially as a lover of those arts and sciences which do so much to adorn it. On September 14, 1859, I sat on this platform and listened to the eloquent address and wise counsel of the Prince Consort. At one time a member of his household, it was my privilege to co-operate with this illustrious prince in many questions relating to the advancement of science. I naturally, therefoi'e, turned to his presidential address to see whether I might not now continue those counsels which he then gave with all the breadth and comprehensiveness of his masterly speeches. I found, as I expected, a text for my own discourse in some pregnant remarks which he made upon the relation of Science to the State. They are as follows : — 'We may be justified in hoping . . . that the Legislature and the State will more and more recognise the claims of science to their attention, so that it may no longer require the begging-box, but speak to the State like a favoured child to its parent, sure of his paternal solicitude for its welfare ; that the State will recognise in science one of its elements of strength and prosperity, to foster which the clearest dictates of self- interest demand.' This opinion, in its broadest sense, means that the relations of science to the State should be made more intimate because the advance of science is needful to the public weal. The importance of promoting science as a duty of statecraft was well enough known to the ancients, especially to the Greeks and Arabs, but it ceased to be recosjuised in the dark a^es, and was lost to sigrht during the revival of letters in the fifteenth and sixteenth centuries. Germany and France, which are now in such active competition in promoting science, have only publicly acknowledged its national importance in recent times. Even in the last century, though France had its Lavoisier and Germany its Leibnitz, their Governments did not know the value of science. When the former was condemned to deatli in the Reign of Terror, a petition was presented to the rulers that his life might be spared for a few weeks in order that he might complete some important experiments, but the reply was, ' The Republic has no need of savants.' Earlier in the century the much-praised Frederick William of Prussia shouted with a loud voice, during a graduation ceremony in the University of Frankfort, ' An ounce of mother-wit is worth a ton of university wisdom.' Both France and Germany are now ashamed of these utterances of their rulers, and make energetic efforts to advance science with the aid of their national resources. More remarkable is it to see a young nation like the United States reserv- ing large tracts of its national lands for the promotion of scientific education. In some respects this young country is in advance of all 6 ■ EEPORT 1885. Europoan nations in joining science to its administrative offices. Its scientific publications, like the great palteontological work embodying the researches of Professor Marsh and his associates in the Geological Survey, are an example to other Governments. The Minister of Agricul- ture is surrounded with a staff of botanists and chemists. The Home Secretary is aided by a special Scientific Commission to investigate the habits, migrations, and food of fishes, and the latter has at its disposal two specially-constrncted steamers of large tonnage. The United States and Gi'eat Britain i^i-omote fisheries on distinct systems. In this country we are perpetually issuing expensive Commissions to visit the coasts in order to ascertain the experiences of fishermen. I have acted as Chairman of one of these Royal Commissions, and found that the fishermen, having only a knowledge of a small area, gave the most contradictory and unsatisfactory- evidence. In America the questions are put to Nature, and not to fisher- men. Exact and searching investigations are made into the life-history of the fishes, into the temperature of the sea in which they live and spawn, into the nature of their food, and into the habits of their natural enemies. For this purpose the Government give the co-operation of the navy, and provide the Commission with a special corps of skilled naturalists, some of whom go out with the steamships and others work in the biological laboratories at Wood's Holl, Massachusetts, or at Washington. The difierent universities send their best naturalists to aid in these in- vestigations, which are under the direction of Mr. Baird, of the Smith- sonian Institution. The annual cost of the Federal Commission is about 40,000/., while the separate States spend about 2O,O00Z. in local efibrts. The practical results flowing from these scientific investigations have been important. The inland waters and rivers have been stocked with fish of the best and most suitable kinds. Even the great ocean which washes the coasts of the United States is beginning to be afiected by the knowledge thus acquired, and a sensible result is already produced upon the most important of its fisheries. The United Kingdom largely depends upon its fisheries, but as j-et our Government have scarcely realised the value of such scientific investigations as those pursued with success by the United States. Less systematical!}', but with great benefit to science, our own Government has used the surveying expeditions, and sometimes has ec^uipped special expeditions to promote natural history and solar physics. Some of the latter, like the voyage of the ' Challenger,' have added largely to the store of knowledge ; while the former, though not primarily intended for scientific research, have had an indirect result of infinite value by becoming training-schools for such investigators as Edward Forbes, Darwin, Hooker, Huxley, Wyville Thomson, and others. In the United Kingdom we are just beginning to understand the wisdom of Washington's farewell address to his countrymen, when he said : ' Promote as an object of primary importance institutions for the general diffusion of knowledge. In proportion as the structure of a governmeafc ADDRESS. 7 gives force to public opinion, it is essential that public opinion should be enlightened.' It was only in 1870 that our Parliament established a system of national primary education. Secondary education is chaotic, and remains unconnected with the State, while the higher education of the universities is only brought at distant intervals under the view of the State. All great countries except England have Ministers of Education, but this country has only Ministers who are the managers of primary schools. We are inferior even to smaller countries in the absence of organised State supervision of education. Greece, Portugal, Egypt, and Japan have distinct Ministers of Education, and so also among our Colonies have Victoria and New Zealand . Gradually England is gathering materials for the establishment of an efficient Education Minister. The Department of Science and Art is doing excellent work in diffusino- a taste for elementary science among the working classes. There are now about 78,000 persons who annually come under the influence of its science classes, while a small number of about two hundied, many of them teachers, receive thorough instruction i"n science at the excellent school in South Kensington of which Professor Huxley is the Dean. I do not dwell on the work of this Government department, because my object ia chiefly to point out how it is that science lags in its progress in the United Kingdom owing to the deficient interest taken in it hj the middle and upper classes. The working classes are being roused from their indifi'er- ence. They show this by their selection of scientific men as candidates at the next election. Among these are Professors Stuart, Roscoe, Maskelyne, and Riicker. It has its significance that such a humble representative of science as myself received invitations from working-class constituencies in more than a dozen of the leading manufacturing towns. In the next Parliament I do not doubt that a Minister of Education will be created as a nucleus round which the various educational materials may crystallise in a definite form. III. Science and Secondary Education. Various Royal Commissions have made inquiries and issued recom- mendations in regard to our public and endowed schools. The Com- missions of I86I, 1804, 1868, and 1873 have expressed the strongest disapproval of the condition of our schools, and, so far as science is concerned, their state is much the same as when the Duke of Devon- shire's Commission in 1873 reported in the following words : — ' Con- sidering the increasing importance of science to the material interests of the country, we cannot but regard its almost total exclusion from the training of the upper and middle classes as little less than a national mis- fortune.' No doubt there are exceptional cases and some brilliant examples of improvement since these words were written, but generally throughout the country teaching in science is a name rather than a reality. The Technical Commission which reported last year can only point to three schools in Great Britain in which science is fully and adequately taught. 8 REPORT 1885. While tbe Commission gives ns the consolation that England is still in advance as an industrial nation, it warns us that foreign nations, which were not long ago far behind, are now making more rapid progress than this country, and will soon pass it in the race of competition unless we give increased attention to science in public education. A few of the large towns, notably Manchester, Bradford, Hnddersfield, and Birming- ham, are doing so. The working classes are now receiving better instruction in science than the middle classes. The competition of actual life asserts its own conditions, for the children of the latter 6nd inci'easing difficulty in obtaining emjiloyment. The cause of this lies in the fact that the schools for the middle classes have not yet adapted themselves to tbe needs of modern life. It is true that many of the endowed schools have been put under new schemes, but as there is no public supervision or inspection of them, we have no knowledge as to whether they have prospered or slipped back. Many corporate schools have arisen, some of them, like Clifton, Cheltenham, and Marlborough Colleges, doing excellent educational work, though as regards all of them the public have no rights and cannot enforce guarantees for efficiency. A Return just issued, on the motion of Sir John Lubbock, shows a lamentable deficiency in science teaching in a great proportion of the endowed schools. While twelve to sixteen hours per week ars devoted to classics, two to three hours are considered ample for science in a large proportion of the schools. In Scotland there are only six schools in the Return which give more than two hours to science weekly, while in many schools its teaching is wholly omitted. Every other part of the kingdom stands in a better position than Scotland in relation to the science of its endowed schools. The old traditions of education stick as firmly to schools as a limpet does to a rock ; though I do the limpet injustice, for it does make excursions to seek pastui-es new. Are we to give up in despair because an exclusive system of classical education has resisted the assatilts of such cultivated authors as Milton, Montaigne, Cowley, and Locke ? There was once an enlightened Emperor of China, Chi Hwangti, who knew that his country was kept back by its exclusive devotion to the classics of Confucius and Mencius. He invited 500 of the teachers to bring their copies of these authors to Pekin, and after giving a great banquet in their honour, he buried alive the professors along with their manuscripts in a deep pit. But Confucius and j\Ienciu8 still reign supreme. I advocate milder measures, and depend for their adoption on the force of public opinion. The needs of modern life will force schools to adapt themselves to a scientific age. Grammar-schools believe them- selves to be immortal. Those curious immortals — the Struldbrugs — described by Swift, ultimately regretted their immortality, because they found themselves out of touch, sympathy, and fitness with the centuries in which they lived. As there is no use clamouring for an instrument of more compass and power until we have made up our mind as to the tune, Pi'ofessor Huxley, in ADDRESS. 9 his evidence before a Parliamentary Committee in 1884, has given a time- table for grammar-schools. He demands that out of their forty hours for public and private study, ten should be given to modern languages and history, eight to arithmetic and mathematics, six to science, and two to geography, thus leaving fourteen hours to the dead languages. No time- table would, however, be suitable to all schools. The great public schools of England will continue to be the gymnasia for the upper classes, and should devote much of their time to classical and literary culture. Even now they introduce into their curriculum subjects unknown to them when the Royal Commission of 18G8 reported, though they still accept science with timidity. Unfortunately, the other grammar-schools which educate the middle classes look to the higher public schools as a type to which they should conform, although their functions are so different. It is in the interest of the higher public schools that this difference should be recognised, so that, while they give an all-round education and expand their curriculum by a freer recognition of the value of science as an educational power in developing the faculties of the upper classes, the schools for the middle classes should adapt themselves to the needs of their existence, and not keep up a slavish imitation of schools with a different function. The stock argument against the introduction of modern subjects into grammar-schools is that it is better to teach Latin and Greek thoroughly rather than various subjects less completely. But is it true that thoroughness in teaching dead languages is the result of an exclusive system ? In 1868 the Royal Commission stated that even in the few great public schools thoroughness was only given to thirty per cent, of the scholars, at the sacrifice of seventy per cent, who got little benefit from the system. Since then the curriculum has been widened and the teaching has improved. I question the soundness of the principle that it is better to limit the attention of the pupils mainly to Latin and Gi'eek, highly as I value their educational power to a certain order of minds. As in biology the bodily development of animals is from the general to the special, so is it in the mental development of man. In the school a boy should be aided to discover the class of knowledge that is best suited for his mental capacities, so that, in the upper forms of the school and in the university, knowledge maybe specialised in order to cultivate the powers of the man to their fullest extent. Shakspeare's educational formula may not be altogether true, but it contains a broad basis of truth — No profit grows, where is no pleasure ta'en ; — In brief, sii', study what you most affect. The comparative failure of the modern side of school education arises from constituting it out of the boys who are looked upon as classical asses. Milton pointed out that in all schools there are boys to whom the dead languages are ' like thorns and thistles,' which form a poor nourish, ment even for asses. If teachers looked upon these classical asses as beings who might receive mental nurture according to their nature, ]0 REPORT — 1885. mucli higher results ■would follow the bifurcation of our schools. Saul •went out to look for asses and he found a kingdom. Surely this fact is more encouraging than the. example of Gideon, who ' took thorns of the wilderness and briars, and with these he taught the men of Succoth.' ' The adaptation of public schools to a scientific age does not involve a contest as to whether science or classics shall prevail, for both are indispensable to true education. The real question is whether schools will undertake the duty of moulding the minds of boys according to their mental varieties. Classics, from their structural perfection and power of awakening dormant faculties, have claims to precedence in education, but they have none to a practical monopoly. It is by claiming the latter that teachers sacrifice mental recepti^-ity to a Procrustean uniformity. The universities are changing their traditions more rapidly than the schools. The via antiqua which leads to them is still broad, though a via moderna, with branching avenues, is also open to their honours and emoluments. Physical science, which was once neglected, is now encouraged at the universities. As to the seventy per cent, of boys who leave schools for life-work without going through the universities, are there no growing signs of discontent which must force a change ? The Civil Sei'vice, the learned professions, as well as the armj^ and navy, are now barred by examinations. Do the boys of our public schools easily leap over the bars, although some of them have lately been lowered so as to suit the schools ? So difficult are these bars to scholars that crammers take them in hand before they attempt the leap ; and this occurs in spite of the large value attached to the dead languages and the small value placed on modern subjects. Thus, in the Indian Civil Service examina- tions, SOO marks as a maximum are assigned to Latin, GOO to Greek, 500 to chemistry, and 300 to each of the other physical sciences. But if we take the average working of the system for the last four years, we find that while sixty-eight per cent, of the maximum were given to candidates in Greek and Latin, only forty-five pen' cent, were accorded to candidates in chemistry, and but thirty per cent, to the other physical sciences. Schools sending up boys for competition naturally shun subjects which are dealt "with so hardly and so heavily handicapped by the State. Passing from learned or public professions to commerce, how is it that in our great commercial centres, foreigners — German, Swiss, Dutch, and even Greeks — push aside our English youth and take the places of profit which belong to them by national inheritance ? How is it that in our Colonies, like those in South Africa, German enterprise is pushing aside English incapacity ? How is it that we find whole branches of manufactures, when they depend on scientific knowledge, passing away from this country, in which they originated, in order to engraft themselves abroad, although their decaying roots remain at home ? - The answer to ' Judges viii. IG. - See Dr. Perkin.s' address to the Soc. Chem. Industry. 'Nature,' Aug. 6, 1885, p. 333. ADDRESS. 1 1 tliese questions is that our systems of education are still too narrow for the increasing struggle of life. Faraday, who had no narrow vie\YS in regard to education, deplored the future of our youth in the competition of the world, because, as he said with sadness, ' our schoolboys, when they come out of school, are isrnorant of their ignorance at the end of all that education.' The opponents of science education allege that it is not adapted for mental development, because scientific facts are often disjointed and exercise only the memory. Those who argue thus do not know what science is. No doubt an ignorant or half-informed teacher may present science as an accumulation of unconnected facts. At all times and in all subjects there are teachers without a3sthetical or philosophical capacity — men who can only see carbonate of lime in a statue by Phidias or Praxiteles ; who cannot survey zoology on account of its millions of species, or botany because of its 130,000 distinct plants ; men who can look at trees without getting a conception of a forest, and cannot distinguish a stately edifice from its bricks. To teach in that fashion is like going to the tree of science with its glorious fruit in order to pick up a handful of the dry fallen leaves from the ground. It is, however, true that as science teaching has had less lengthened experience than that of literature, its methods of instruction are not so matured. Scientific and literary teaching have difiierent methods ; for while the teacher of literature rests on authority and on books for his guidance, the teacher of science discards authority and depends on facts at first hand, and on the book of Nature for their interpretation. Natural science more and more resolves itself into the teaching of the laboratory. In this way it can be used as a powerful means of quickening observation, and of creating a faculty of induction after the manner of Zadig, the Babylonian described by Voltaire. Thus facts become surrounded by scientific conceptions, and are subordinated to order and law. It is not those who desire to unite literature with science who degrade education ; the degradation is the consequence of the refusal. A violent reaction — too violent to be wise — has lately taken place against classical education in France, where their own vernacular occupies the position of dead languages, while Latin and science are given the same time in the curriculum. In England manufacturers cry out for technical education, in which classical culture shall be excluded. In the schools of the middle classes science rather than technics is needed, because, when the seeds of science are sown, technics as its fruit will appear at the appointed time. Epictetus was wise when he told us to observe that, though sheep eat grass, it is not grass but wool that grows on their backs. Should, how- ever, our grammar-schools persist in their refusal to adapt themselves to the needs of a scientific age, England must follow the example of other European nations and found new modern schools in competition with them. For, as Huxley has put it, we cannot continue in this age ' of full modern artillery to turn out our boys to do battle in it, equipped only 12 KEPOET — 1885. with the sword and shield of an ancient gladiator.' In a scientific and keenly competitive age an exclusive education in the dead languages is a perplexing anomaly. The flowers of literature should be cultivated and gathered, though it is not wise to send men into our fields of industry to gather the harvest when they have been taught only to cull the poppies and to push aside the wheat. IV. Science and the Universities. The Stale has always felt bound to alter and improve universities, even when their endowments are so large as to render it unnecessary to support them by public funds. When universities are poor, Parliament gives aid to them from imperial taxation. In this country that aid has been given with a very spaiing hand. Thus the universities and colleges of Ireland have received about thirty thousand pounds annually, and tbo same sum has been granted to the four universities of Scotland. Com- pared Avith imperial aid to foreign universities such sums are small. A single German university like Strasburg or Leipsic receives above 40,000Z. annually, or 10,000/. more than the whole colleges of Ireland or of Scotland. Strasburg, for instance, has had her university and its libraiy rebuilt at a cost of 711,000Z., and receives an annual subscription of 43,000Z. In rebuilding the university of Strasburg eight laboratories have been provided, so as to equip it fully with the modern requirements for teaching and reseai'ch.' Prussia, the most economical nation in the world, spends 391,000/. yearly out of taxation on her universities. The recent action of France is still more remarkable. After the Franco-German War the Institute of France discussed the important question : — ' Poui'quoi la France n'a pas trouve d'hommes superieurs au moment du \)(:v\\ ? ' The general answer was because France had allowed university education to sink to a low ebb. Before the great Revolution France had twenty-thi'ee autonomous universities in the provinces. Xapoleon desired to found one great university at Paris, and he crushed out the others with the hand of a despot, and remodelled the last with the instincts of a drill-sergeant. The central university sank so low that in 1868 it is said that only 8,000/. were spent for true academic purposes. Startled by the intellectual sterility shown in the war, France has made gigantic eiforts to retrieve her position, and has rebuilt the provincial colleges at a cost of 3,280,000/., while her annual budget for their support now reaches half a million of pounds. In order to open these provincial colleges to the best talent of France, more than five hundred scholarships have been founded at an annual cost of 30,000/. France now recognises that it is not by the number of men under arms that she can compete with her great neighbour Germany, so she has determined to equal her in intellect. ' The cost of these laboratories has been as follows : — Chemical Institute, 35,000Z. ; Physical Institute, 28,000Z. ; Botanical Institute, 2G,000Z. ; Observatory, 25,000?. ; Anatomy, 42,000/.; Clinical Surgery, 26,000/.; Physiological Chemistry, 16,000/.; Physiological Institute, 13,900/, ADDRESS. 13 Tou will understand why it is that Germany was obliged, even if slie had not been willing, to spend sach large sums in order to equip the university of her conquered province, Alsace- Lorraine. France and Germany are fully aware that science is the source of wealth and power, and that the only way of advancing it is to encourage universities to make researches and to spread existing knowledge through the community. Other European nations are advancing on the same lines. Switzerland is a remarkable illustration of how a country can compensate itself for its natural disadvantages by a scientific education of its people. Switzerland contains neither coal nor the ordinary raw materials of industry, and is separated from other countries which might supply them by mountain barriers. Yet, by a singularly good system of graded schools, and by the great technical college of Ziirich, she has become a prosperous manufac- turing country. In Great Britain we have nothing comparable to thia technical college, either in magnitude or efScieucy. Belgium is reor- ganising its universities, and the State has freed the localities from the charge of buildings, and will in future equip the universities with efficient teaching resources out of public taxation. Holland, with a population of 4,000,000 and a small revenue of 9,000,000/., spends 13G,O0OZ. on her four universities. Contrast this liberality of foreign countries in the promotion of higher instruction with the action of our own country. Scotland, like Holland, has four universities, and is not very different from it in population, but it only receives 30,000/. from the Slate. By a special clause in the Scotch Universities Bill the Governm_ent asked Parliament to declare that under no circumstances should the Parlia- mentary grant be ever increased above 40,000?. According to the views of the British Treasury there is a finality in science and in expandino- knowledge. The wealthy universities of Oxford and Cambridge are gradually con- structing laboratories for science. The merchant princes of Manchester have equipped their new Victoria University with similar laboratories. Edinburgh and Glasgow Universities have also done so, partly at the cost of Government and largely by private subscriptions. The poorer universities of Aberdeen and St. Andrews are still inefficiently provided with the modern appliances for teaching science. London has one small Government college and two chartered colleo-es, but is wholly destitute of a teaching university. It would excite o-reat astonishment at the Treasury if we were to make the modest request that the great metropolis, with a population of four millions, should be put into as efficient academical position as the town of Strasburg, with 104,000 inhabitants, by receiving, as that town does, 43,000/. annually for academic instruction, and 700,000/. for university buildings. Still, the amazing anomaly that London has no teaching university must ere long cease. It is a comforting fact that, in spite of the indifference of Parliament, the large towns of the kingdom are showing their sense of the need of 14 EEPOET — 1885. higher education. Manchester has already its university. Nottingham, Birmingham, Leeds, and Bristol have colleges more or less complete. Liverpool converts a disused lunatic asylum into a college for sane people. Cardiff rents an infirmary for a collegiate building. Dundee, by private benefaction, rears a Baxter College with larger ambitions. All these are healthy signs that the public are determined to have advanced science teachinc ; but the resources of the institutions are altogether inadequate to the end in view. Even in the few cases where the laboratories are effi- cient for teachino- purposes, they are inefficient as laboratories for research. Under these circumstances the Royal Commission on Science advocates special Government laboratories for research. Such laboratories, sup- ported by public money, are as legitimate subjects for expenditure as "alleries for pictures or sculpture ; but I think that they would not be successful, and would injure science if they failed. It would be safer in the meantime if the State assisted universities or well-established colleges to found laboratories of research under their own care. Even such a proposal shocks our Chancellor of the Exchequer, who tells us that this country is burdened with public debt, and has ironclads to build and arsenals to provide. Nevertheless our wealth is proportionally much greater than that of foreign States which are competing with so much vigour in the promotion of higher education. They deem such expenditure to be true economy, and do not allow their huge standing armies to be an apology for keeping their people backwards in the march of knowledge. France, which in the last ten years has been spending a million annually on university education, had a war indemnity to pay, and competes suc- cessfully with this country in ironclads. Either all foreign States are strano-ely deceived in their belief that the competition of the world has become a competition of intellect, or we are marvellously unobservant of J the change which is passing over Europe in the higher education of the ^ people. Preparations for war will not ensure to us the blessings and | security of an enlightened peace. Protective expenditure may be wise, thongh productive expenditure is wiser. Were half the powers which fill the worlrl with terror, AVere half the wealth bestowed on camps and courts, Given to redeem the human mind from error^ There were no need of arsenals and forts. Universities are not mere storehouses of knowledge ; they are also conservatories for its cultivation. In Mexico there is a species of ant which sets apart some of its individuals to act as honey-jars by monstrously extending their abdomens to store the precious fluid till it is wanted by the community. Professors in a university have a higher function, because they ought to make new honey as well as to store it. The widening of the bounds of knowledge, literary or scientific, is the crown- ino- o-lory of university life. Germany unites the functions of teaching and research in the universities, while France keeps them in separate institutions. The former system is best adapted to our habits, but its ADDRESS. 15 condition for success is tliafc our science chairs should be greatly increased, so that teachers should not be wholly absorbed in the duties of instruc- tion. Germany subdivides the sciences into various chairs, and gives to the professors special laboratories. It also makes it a condition for the higher honours of a university that the candidates shall give proofs cf their ability to make original researches. Under such a system, teaching and investigation are not incompatible. In the evidence before the Science Commission many opinions were given that scientific men en- gaged in research should not be burdened with the duties of education, and there is much to be said in support of this view when a sino-le professor for the whole range of a physical science is its only represen- tative in a university. But I hope that such a system will not long continue, for if it do we must occupy a very inferiar position as a nation in the intellectual competition of Europe. Research and education in limited branches of higher knowledge are not incompatible. It is true that Gahleo complained of the burden imposed upon him by his numerous astronomical pupils, though few other philosophers have echoed this com- plaint. Newton, who produced order in worlds, and Dalton, who brought atoms under the reign of order and number, rejoiced in their pupils. Lalande spread astronomers as Liebig spread chemists, and Johannes Miiller biologists, all over the world. Laplace, La Grange, Dulong, Gay Lussac, Berthollet, and Dumas were professors as well as discoverers in France. In England our discoverers have generally been teachers. In fact I recollect only three notable examples of men who were not — Boyle, Cavendish, and Joule. It was so in ancient as well as in modern times, for Plato and Aristotle taught and philosophised. If you do not make the investigator a schoolmaster, as Dalton was, and as practically our professors are at the present time, with the duty of teaching all branches of their sciences, the mere elementary truths as well as the highest generalisations being compressed into a course, ifc is well that they should be brought into contact with the world in which they live, so as to know its wants and aspirations. They could then quicken the pregnant minds around them, and extend to others their own power and love of research. Goethe had a fine perception of this when he wrote — Wer in cTer Weltgeschichte lebt, Wer in die Zeiten schaut, und strebt, Nur der ist werth, zu sprechen und zu dichtcn. Our universities are still far from the attainment of a proper com- bination of their resources between teaching and research. Even Oxford and Cambridge, which have done so much in recent years in the equip- ment of laboratories and in adding to their scientific stafP, are still far behind a second-class German university. The professional faculties of the English universities are growing, and will dififuse a greater taste for science among their students, though they may absorb the time of the limited professoriate so as to prevent it advancing the boundaries of 16 REPORT — 1885. knowledo-e. Professional faculties are absolutely essential to tbe existence of universities in poor countries like Scotland and Ireland. This L.is been the case from the early days of the Bologna University up to the present time. Originally universities arose not by mere bulls of popes, but as a response to the strong desire of the professional classes to dignify their crafts by real knowledge. If their education had been limited to mere technical schools like the Medical School of Salerno which flourished in the eleventh century, length but not breadth would have been given to education. So the universities wisely joined culture to the professional ociences. Poor countries like Scotland and Ireland must have their academic systems based on the professional faculties, although wealthy universities like Oxford and Cambridge may continue to have them as mere supplements to a more general education. A greater liberality of support on the part of the State in the establishment of chairs of science, for the sake of science and not merely for the teaching of the professions, would enable the poorer universities to take their part in the advancement of knowledge. I have already alluded to the foundation of new colleges in different parts of the kingdom. Owens College has worthily developed into the Victoria University. Formerly she depended for degrees on the University of London. No longer will she be like a moon reflecting cold and sickly rays from a distant luminary, for in future she will be a sun, a centre of intelligence, warming and illuminating the regions around her. The other colleges which have formed themselves in large manufacturing districts are remarkable expressions from them that science must be promoted. Including the colleges of a high class, such as University College and King's College in London, and the three Queen's Colleges in Ireland, the aggregate attendance of students in colleges without university rank is between nine and ten thousand, while that of the universities is fifteen thousand. No doubt some of the provincial colleges require considerable improvement in their teaching methods; sometimes they unwisely aim at a full university curriculum when it would be better for them to act as faculties. Still they are all growing in the spirit of self- help, and some of them are destined, like Owens College, to develop into universities. This is not a subject of alarm to lovers of education, while it is one of hope and encouragement to the great centres of industry. There are too few autonomous universities in England in proportion to its population. "While Scotland, with a population of 3J millions, has four universities with 6,500 students, England, with 26 millions of people, has only the same number of teaching universities with 6,000 students. Unless English colleges have such ambition, they may be turned into mere mills to grind out material for examinations and competitions. Higher colleges should always hold before their students that knowledge, for its own sake, is the only object worthy of reverence. Beyond college life there is a land of research flowing with milk and honey for those who know how to cultivate it. ADDRESS. 1 1 Colleges should at least show a Pisgah view of this Land of Promise, which stretches far beyond the Jordan of examinations and competitions. V. Science and Inclustnj, In the popular mind the value of science is measured by its applica- tions to the useful purposes of life. It is no doubt true that science wears a beautiful aspect when she confers practical benefits upon man. But truer relations of science to industry are implied in Greek mythology. Vulcan, the god of industry, wooed science, in the form of Minerva, with a passionate love, but the chaste goddess never married, although she conferi'ed upon mankind nearly as many arts as Prometheus, who, like other inventors, saw civilisation progressing by their use while he lay groaning in want on Mount Caucasus. The rapid development of industry in modern days depends on the applications of scientific knowledge, while its slower growth in former times was due to experiments being made by trial and error in order to gratify the needs of man. Then an experiment was less a questioning of Nature than an exercise on the mind of the experimentalist. For a true questioning of Nature only arises when intellectual conceptions of the causes of phenomena attach themselves to ascertained facts as well as to their natural environments. Much real science had at one time accumulated in Egypt, Greece, Rome, and Arabia, though it became obscured by the intellectual darkness which spread over Europe like a pall for many centuries. The mental results of Greek science, filtered through the Romans and Arabians, gradually fertilised the soil of Europe. Even in ages which are deemed to be dark and un- prolific, substantial though slow progress was made. By the end of the fifteenth century the mathematics of the Alexandrian school had become the possession of Western Europe ; Arabic numerals, algebra, trigo- nometry, decimal reckoning, and an improved calendar having been added to its stock of knowledgre. The old discoveries of Democritus and Archimedes in physics, and of Hipparchus and Ptolemy in astronomy, were producing their natural developments, though with great slowness. Many manufactui'es, growing chiefly by experience, and occasionally lightened up by glimmerings of science throughout the prevailing dark- ness, had arisen before the sixteenth century. A knowledge of the pro- perties of bodies, though scarcely of their relations to each other, came through the labours of the alchemists, who had a mighty impulse to work, for by the philosopher's stone, often not larger than half a rape- seed, they hoped to attain the three sensuous conditions of human enjoy- ment, gold, health, and immortality. By the end of the fifteenth century many important manufactures were founded by empirical experiment, with only the uncertain guidance of science. Among these were the compass, printing, paper, gunpowder, guns, watches, forks, knitting- needles, horseshoes, bells, wood cutting and copper engraving, wire- drawing, steel, table glass, spectacles, mici-oscopes, glass mirrors backed by amalgams of tin and lead, windmills, crushing and saw mills. These 1885. c 18 REPora- — 1835. important manufactures arose from an increased knowledge of facts, around whicli scientific conceptions were slowly concreting. Aristotle defines this as science when he says, ' Art begins when, from a great number of experiences, one genei'al conception is formed which will embrace all similar cases.' Such conceptions are formed only when culture develops the human mind and compels it to give a rational account of the world in which man lives, and of the objects in and around it, as well as of the phenomena which govern their action and evolution. Though the accumulation of facts is indispensable to the growtb of science, a thousand facts are of less value to human progress than is a single one when it is scientifically comprehended, for it then becomes generalised in all similar cases. Isolated facts may be viewed as the dust of science. The dust which floats in the atmosphere is to the common observer mere incoherent matter in a wrong place, while to the man of science it is all-important when the rays of heat and light act upon its floating particles. It is by them that clouds and rains are influenced ; it is by their selective influence on the solar waves that the blue of the heavens and the beauteous colours of the sky glorify all Nature. So, also, ascertained though isolated facts, forming the dust of science, become th.e reflecting media of the light of knowledge, and cause all Nature to assume a new a.spect. It is with the light of knowledge that we are enabled to question Nature through direct experiment. The hypothesis or theory which induces us to put tlie ex- perimental question maybe right or wrong; still, ^)-?(c?e>is qiiestio dimidium scienticB est — it is half way to knowledge when you know what you have to inquire. Davy described hypothesis as the mere scafiblding of science, useful to build up true knowledge, but capable of being put up or taken down at pleasure. Undoubtedly a theory is only temporary, and the reason is, as Bacon has said, that the man of science ' loveth truth more than his theory.' The changing theories which the world despises are the leaves of the tree of science drawing nutriment to the parent stems, and enabling it to put forth new branches and to produce f I'uit ; and though the leaves fall and decay, the very products of decay nourish the roots of the tree and reappear in the new leaves or theories which succeed. When the questioning of Nature by intelligent experiment has raised a system of science, then those men who desire to apply it to industrial inventions proceed by the same methods to make rapid progress in the arts. They also must have means to compel Nature to reveal her secrets, ^neas succeeded in his great enterprise by plucking a golden branch from the tree of science. Armed with this even dread Charon dared not refuse a passage across the Styx ; and the gate of the Elysian fields was unbarred when he hung the branch on its portal. Then new aspects of Nature were revealed — Another sun and stars they know That shine like ours, but shine below. It is by carrying such a golden branch from the tree of science that in- ADDEESS. 1 9 rentors are able to advance the arts. In illustration of bow slowly at first and bow rapidly afterwards science and its applications arise, I will take only two out of thousands of examples which lie ready to my hand. One of the most familiar instances is air, for that surely should have been soon understood if man's unaided senses are sufficient for knowledge. Air has been under the notice of mankind ever since the first man drew bis first breath. It meets him at every turn ; it fans him with gentle breezes, and it buffets him with storms. And yet it is certain that this familiar object — air — is very imperfectly understood up to the present time. We now know by recent researches that air can be liquefied by pressure and cold ; but as a child still looks upon air as nothing, so did man in his early state. A vessel filled with air was deemed to be empty. But man, as soon as he began to speculate, felt the importance of air, and deemed it to be a soul of the world upon which the respiration of man and the god-like quality of fire depended. Yet a really intelligent conception of these two essential conditions to man's existence — respiration and com- bustion — was not formed till about a century ago (1 775). No doubt long before that time there had been abundant speculations regarding air. Anaximenes, 548 years before Christ, and Diogenes of Apollonia, a century later, studied the properties of air so far as their senses would allow them ; so, in fact, did Aristotle. Actual scientific experiments were made on air about the year 1100 by a remarkable Saracen, Alhazen, who ascertained important truths which enabled Galileo, Torricelli, Otto de Guericke, and others at a later period to discover laws leading to important practical applications. Still there was no intelligent conception as to the compo- sition of air until Priestley in 1774 i*epeated, with the light of science, an empirical observation which Eck de Sulbach had made three hundred years before upon the union of mercury with an ingredient of air and the decomposition of this compound by heat. This experiment now proved that the active element in air is oxygen. From that date our knowledge, derived from an intelligent questioning of air by direct experiments, has gone on by leaps and bounds. The air, which mainly consists of nitrogen and oxygen, is now known to contain carbonic acid, ammonia, nitric acid, ozone, besides hosts of living organisms which have a vast influence for good or evil in the economy of the world. These micro-organisms, the latest contribution to our knowledge of air, perform great analytical functions in organic nature, and are the means of converting much of its potential energy into actual energy. Through their action on dead matter the mutual dependence of plants and animals is secured, so that the air becomes at once the grave of organic death and the cradle of organic life. No doubt the ancients suspected this without being able to prove the de- pendence. Euripides seems to have seen it deductively when he describes the results of decay : — Then that which springs from earth, to earth returns, And that which draws its being from the sky Eises again up to the skyey height C 2 20 REPORT — 1885. Tlie consequences of the progressive discoveries have added largely to our knowledge of life, and have given a marvellous development to the industrial arts. Combustion and respiration govern a wide range of processes. The economical use of fuel, the growth of plants, the food of animals, the processes of husbandry, the maintenance of public health, the orio-in and cure of disease, the production of alcoholic drinks, the processes of making vinegar and saltpetre — all these and many other kinds of knowied"-e have been brought under the dominion of law. No doubt animals respired, fuel burned, plants grew, sugar fermented, before Tve knew how they depended upon air. But as the knowledge was empirical, it could not be intelligently directed. Now all these processes are ranched in order under a wise economy of Nature, and can be directed to the utilities of life ; for it is trup, as Swedenborg says, that ' human ends always ascend as Nature descends.' There is scarcely a large industry in the world which has not received a mighty impulse by the better knowledge of air acquired within a hundred years. If I had time I could show still more strikingly the industrial advantages which have followed from Cavendish's discovery of the composition of water. I wish that I could have done this, because it was Addison who foolishly said, and Paley who as unwisely approved the remark, ' that mankind required to know no more about water than the temperature at which it froze and boiled, and the mode of making steam.' "When we examine the order of progress in the arts, even before they are illumined by science, their improvements seem to be the resultants of three conditions. 1. The substitution of natural forces for brute aiiimal power, as when Hercules used the waters of the Alpheus to cleanse the Augean stables; or when a Kamchadal of Eastern Asia, who has been three years hollowing out a canoe, finds that he can do it in a few hours by fire. 2. The economy of time, as when a calendering machine produces the same gloss to miles of calico that an African savage gives to a few inches by rubbing it with the shell of a snail ; or the economy of produc- tion, as when steel pens, sold when first introduced at one shilling apiece, are now sold at a penny per dozen ; or when steel rails, lately costing 45Z. per ton, can now be sold at 5/. 3. Methods of utilising waste products, or of endowing them with properties which render them of increased valae to industry, as when waste scrap iron and the galls on the oak are converted into ink ; or the badly-smelling waste of gasworks is transformed into fragrant essences, brilliant dyes, and fertilising manure ; or when the efl'ete matter of animals or old bones is changed into lucifcr-matches. All three results are often combined when a single end is obtained — at all events, economy of time and production invariably follows when natural forces substitute brute animal force. In industrial progress the sweat of the brow is lessened by the conceptions of the brain. How ADDRESS. 21 exultant is the old Greek poet, Antipater,' when women are relieved of the drudgery of turning the grindstones for the daily supply of corn. ' Woman ! you who have hitherto had to grind corn, let your arms rest for the future. It is no longer for you that the birds announce by their songs the dawn of the morning. Ceres has ordered the loater-nymplis to move the heavy millstones and perform your labour.' Penelope had twelve slaves to grind corn for her small household. During the most prosperous time of Athens it was estimated that there were twenty slaves to each free citizen. Slaves are mere machines, and machines neither invent nor discover. The bondmen of the Jews, the helots of Sparta, the captive slaves of Rome, the serfs of Europe, and uneducated labourers of the present day who are the slaves of ignorance have added nothing to human progress. But as natural forces substitute and become cheaper than slave labour, liberty follows advancing civilisation. Machines require educated superintendence. One shoe factory in Boston by its machines does the work of thirty thousand shoemakers in Paris who have still to go through the weary drudgery of mechanical labour. The steam power of the world, during the last twenty years, has risen from 11^ million to 29 million horse-power, or 152 per cent. Let me take a single example of how even a petty manufacture improved by the teachings of science affects the comforts and enlarges the resources of mankind. When I was a boy, the only way of obtaining a light was by the tinder-box, with its quadruple materials, flint and steel, burnt rags or tinder, and a sulphur-match. If everything went well, if the box could be found and the air was dry, a light could be obtained in two minutes ; but xerj often the time occupied was much longer, and the process became a great trial to the serenity of temper. The consequence of this was that a fire or a burning lamp was kept alight through the day. Old Gerard, in his Herbal, tells us how certain fungi were used to carry fire from one part of the country to the other. The tinder-box long held its position as a great discovery in the arts. The Pyxidicula Igniaria of the Romans appears to have been much the same implement as, though a little ruder than, the flint and steel which Philip the Good put into the collar of the Golden Fleece in 1429 as a representation of high knowledge in the progress of the arts. It continued to prevail till 1833, when phosphorus-matches were introduced ; though I have been amused to find that there are a few venerable ancients in London who still stick to the tinder-box, and for whom a few shops keep a small supply. Phosphorus was no new discovery, for it had been obtained by an Arabian called Bechel in the eighth century. However, it was for- gotten, and was rediscovered by Brandt, who made it out of very stinking materials in 1G69. Other discoveries had, however, to be made before it could be used for lucifer-matches. The science of com- bustion was only developed on the discovery of oxygen a century later. Time had to elapse before chemical analysis showed the kind of bodies ' Analecta Veterum Gracorum, Epig. 39, vol. ii. p. 119. 22 EEroiiT — 1885. ■whicli could be added to phosphorus so as to make it ignite readily. So it Tvas not till 1833 that matches became a partial success. Intolerably bad they then were, dangerously inflammable, horribly poisonous to the makers and injurious to the lungs of the consumers. It required another discovery by Schrotter in 1845 to change poisonous waxy into innocuous red-brick phosphorus in order that these defects might be remedied, and to give us the safety-match of the present day. Now what have these successive discoveries in science done for the nation, in this single manu- facture, by an economy of time ? If before 1833 we had made the same demands for light that we now do, when we daily consume eight matches per head of the population, the tinder-box could have sujjplied the de- mand under the most favourable conditions by an expenditure of one quarter of an hour. The lucifer-match supplies a light in fifteen seconds on each occasion, or in two minutes for the whole day. Putting these differences into a year, the venerable ancient who still sticks to his tinder-box would require to spend ninety hours yearly in the production of light, while the user of lucifer-matches spends twelve hours; so that the latter has an economy of seventy-eight hours yearly, or about ten working days. Measured by cost of production at one shilling and six- pence daily, the economy of time represented in money to our population is twenty-six millions of pounds annually. This is a curious instance of the manner in which science leads to economy of time and wealth even in a small manufacture. In larger industries the economy of time and labour produced by the application of scientific discoveries is beyond all measure- ment. Thus the discovery of latent heat by Black led to the inventions of Watt ; while that of the mechanical equivalent of heat by Joule has been the basis of the progressive improvements in the steam-engine which enables power to be obtained by a consumption of fuel less than one- fourth the amount used twenty years ago. It may be that the engines of Watt and Stephenson will yield in their turn to more economical motors ; still they have already expanded the wealth, resources, and even the terri- tories of England more than all the battles fought by her soldiers or all the treaties negotiated by her diplomatists. The coal which has hitherto been the chief soTirce of power probably re- presents the product of five or six million years during which the sun shone upon the plants of the Carboniferous Period, and stored up its energy in this convenient form. But we are using this conserved force wastefuUy and prodigally ; for, although horse-power in steam engines has so largely in- creased since 1864, two men only now produce what three men did at that date. It is only three hundred years since we became a manufactur- ing country. According to Professor Dewar, in less than two hundred years more the coal of this country will be wholly exhausted, and in half that time will be difficult to procure. Our not very distant descendants will have to face the problem — What will be the condition of England without coal ? The answer to that question depends u^dou the intel- lectual development of the nation at that time. The value of the in- ADDEESS. 23 tellcctual factor of production is continually increasing ; wliilc the values of rav,' material and fuel are lessening factors. It may be that when tlie dreaded time of exhansted fuel Las arrived, its importation from other coal-fields, such as those of New South Wales, will be so easy and cheap that the increased technical education of our operatives may largely over- balance the disadvantages of increased cost in fuel. But this supposes that future Governments in England will have more enlightened views as to the value of science than past Governments have possessed. Industrial applications are but the overflowings of science welling over from the fulness of its measnre. Few would ask now, as was con- stantly done a few years ago, ' What is the use of an abstract discovery in science ? ' Faraday once answered this question by another, ' What is the use of a baby ? ' Yet round that baby centre all the hopes and sentiments of his parents, and even the interests of the State, which interferes in its upbringing so as to ensure it being a capable citizen. The pi-ocesses of mind which produce a discovery or an invention are rarely associated in the same person, for while the discoverer seeks to explain causes and the relations of phenomena, the inventor aims at pro- ducing new effects, or at least of obtaining them in a novel and efficient way. In this the inventor may sometimes succeed without much know- ledge of science, though his labours are infinitely more productive when he understands the causes of the effects which he desires to produce. A nation in its industrial progress, when the competition of the world is keen, cannot stand still. Three conditions only are possible for it. It may go forward, retrogi-ade, or perish. Its extinction as a great nation follows its neglect of higher education, for, as described in the proverb of Solomon, ' They that hate instruction love death.' In sociology, as in biology, there are three states. The first of balance, when things grow neither better nor worse ; the second that of elaboration or evolution, as we see it when animals adapt themselves to their environments ; and the third, that of degeneration, when they rapidly lose the ground they have made. For a nation, a state of balance is only possible in the early stage of its existence, but it is impossible when its environments are constantly changing. The possession of the raw materials of industry and the existence of a surplus population are important factors for the growth of manufactures in the early history of a nation, but afterwards they are bound up with another factor — -the application of intellect to their development. England could not be called a manufacturing nation till the Elizabethan age. No ■doubt coal, iron, and wool were in abundance, though, in the reign of the Plantagenets, they produced little pi'osperity. Wool was sent to Flanders to be manufactured, for England then stood to Holland as Australia now does to Yorkshire. The political crimes of Spain from the reign of Ferdinand and Isabella to that of Philip HI. destroyed it as a great manufacturing nation, and indirectly led to England taking its position. Spain, through the activity and science of the Arabian intellect, 24 EBPORT — 1885. bad acquired many important industries. The Moors and the Moriscoes, who had been in Spain for a period as long as from the Norman Conquest of this country to the present date, were banished, and with them departed the intellect of Spain. Then the invasion of the Low Countries by Philip II. drove the Flemish manufacturers to England, while the French persecution of the Huguenots added new manufacturing experience, and with them came the industries of cotton, wool, and silk. Cotton mixed with linen and wool became freely used, but it was only from 1738 to the end of the century that the inventions of Wyatt, Arkwright, Hargreaves, Crompton, and Cartwright started the wonderful modern development. The raw cotton was imported from India or America, but that fact as regards cost was a small factor in comparison with the intellect required to convert it into a utility. Science has in the last hundred years altered altogether the old conditions of industrial competition. She has taught the rigid metals to convey and record our thoughts even to the most distant lands, and, within less limits, to reproduce our speech. This mai'vellous application of electricity has diminished the cares and responsibilities of Governments, while it has at the same time altered the whole practice of commerce. To England steam and electricity have been of incalculable advantage. The ocean, which once made the coun- try insular and isolated, is now the very life-blood of England and of the greater England beyond the seas. As in the human body the blood bathes all its parts, and through its travelling corpuscles carries force to all its members, so in the body politic of England and its pelagic exten- sions, steam has become the circulatory and electricity the nervous system. The colonies, being young countries, value their raw materials as their chief sources of wealth. "When they become older they will dis- cover it is not in these, but in the cultui'e of scientific intellect, that their future prosperity depends. Older nations recognise this as the law of progress more than we do ; or, as Jules Simon tersely puts it — ' That nation which most educates her people will become the greatest nation, if not to-day, certainly to-morrow.' Higher education is the condition of higher prosperity, and the nation which neglects to develop the intel- lectual factor of production must degenerate, for it cannot stand still. If we felt compelled to adopt the test of science given by Comte, that its value must be measured by fecundity, it might be prudent to claim indus- trial inventions as the immediate fruit of the tree of science, though only fruit which the prolific tree has shed. But the test is untrue in the sense indicated, or rather the fruit, according to the simile of Bacon, is like the golden apples which Aphrodite gave to the suitor of Atalanta, who lagged in her course by stooping to pick them up, and so lost the race. The true cultivators of the tree of science must seek their own reward by seeing it flourish, and let others devote their attention to the possible practical advantages which may result from their labours. There is, however, one intimate connection between science and in- dustry which I hope will be more intimate as scientific education becomes ADDRESS. 25 more prevalent in our scliools and universities. Abstract science depends on the support of men of leisure, either themselves possessing or having provided for them the means of living without entering into the pursuits of active industry. The pursuit of science requires a superfluity of wealth in a community beyond the needs of ordinary life. Such superfluity is also necessary for art, though a picture or a statue is a saleable commodity, while an abstract discovery in science has no immediate or, as regards the discoverer, proximate commercial value. In Greece, when philo- sophical and scientific speculation was at its highest pomt, and when education was conducted in its own vernacular and not through dead languages, science, industry, and commerce wei-e actively prosperous. Corinth carried on the manufactures of Birmingham and Sheffield, while Athens combined those of Leeds, Staffordshire, and London, for it had ■woollen manufactures, potteries, gold and silver work, as well as ship- building. Their philosophers were the sons of biarghers, and sometimes carried on the trades of their fathers. Thales was a travelling oil merchant, who brought back science as well as oil from Egypt. Solon and his great descendant Plato, as well as Zeno, were men of commerce. Socrates was a stone-mason ; Thucydides a gold-miner ; Aristotle kept a druggist's shop until Alexander endowed him with the wealth of Asia. All but Socrates had a superfluity of wealth, and he was supported by that of others. Now if our universities and schools created that love of science which a broad education would surely inspire, our men of riches and leisure who advance the boundaries of scientific knowledge could not be counted on the fingers as they now are, when we think of Boyle, Cavendish, Napier, Lyell, Murchison, and Darwin, but would be as numerous as our statesmen and orators. Statesmen, without a following of the people who share their views and back their work, would be feeble indeed. But while England has never lacked leaders in science, they have too few followers to risk a rapid march. We might create an army to support our generals in science, as Germany has done, and as France is now doing, if education in this country would only m.ould itself to the needs of a scientific age. It is with this feeling that Horace Mann wrote :— ' The action of the mind is like the action of fire ; one billet of wood will hardly burn alone, though as dry as the sun and north-west wind can make it, and though placed in a current of air ; ten such billets will burn well together, but a hundred will create a heat fifty times as intense as ten — will make a current of air to fan their own flame, and consume even greenness itself.' VI. Abstract Science the Condition for Progress. The subject of my address has been the relations of science to the public weal. That is a very old subject to select for the year 1885. I began it by quoting the words of an illustrious prince, the consort of our Queen, who addressed us on the same subject from this platform twenty-six years ago. But he was not the first prince who saw how closely science 26 REPORT — 1885. is bound uj^ with the Avelfare of States. AH, the son-in-law of Mahomet, the fourth successor to the Caliphate, urged upon his followers that men of science and their disciples give security to human progress. Ali loved to say, ' Eminence in science is the highest of honours,' and ' He dies not who gives life to learning.' In addressing you upon texts such as these, my purpose was to show how unwise it is for England to lag in the onward march of science when most other European Powers are using the resources of their States to promote higher education and to advance the boundaries of knowledge. English Governments alone fail to grasp the fact that the competition of the world has become a competition in intellect. !Much of this indifierence is due to our systems of education. I have ill fulfilled my purpose if, in claiming for science a larger share in public education, I have in any way depreciated literature, art, or philo- sophy, for every subject which adds to culture aids in human develop- ment. I only contend that in public education thei-e should be a free play to the scientific faculty, so that the youths who possess it should leai-n the richness of their possession during the educative process. The same faculties which make a man great in any walk of life — strong love of truth, high imagination tempered by judgment, a vivid memory which can co-ordinate other facts with those under immediate consideration— all these are qualities which the poet, the philosopher, the man of literature, and the man of science equally require and should cultivate through all parts of their education as well as in their future careers. My contention is that science should not be practically shut out from the view of a youth while his education is in progress, for the public weal requires that a large number of scientific men should belong to the community. This is necessary- because science has impressed its character upon the age in which we live, and as science is not stationary but progressive, men are re- quired to advance its boundaries, acting as pioneers in the onward march of States. Human progress is so identified with scientific thought, both in its conception and realisation, that it seems as if they were alternative terms in the history of civilisation. In literature, and even in art, a standard of excellence has been attained which we are content to imitate because we have been unable to surpass. But there is no such standard in science. Formerly, when the dark cloud was being dissipated which had obscured the learning of Gi-eece and Rome, the diffusion of literature or the discovery of lost authors had a marked influence on advancing civilisation. Now, a Chrysoloras might teach Greek in the Italian uni- versities without hastening sensibly the onward march of Italy ; a Poggio might discover copies of Lucretius and Quintilian without exercising a tithe of the influence on modern life that an invention by Stephenson or Wheatstone would produce. Nevertheless, the divorce of culture and science, which the present state of education in this country tends to produce, is deeply to be deplored, because a cultured intelligence adds greatly to the development of the scientific faculty. My argument is that no amount of learning without science suffices in the present state ADDRESS. 27 of the world to put us in a position wliicli will enable England to keep ahead or even on a level with foreign nations as regards knowledge and its applications to the utilities of life. Take the example of any man of learning, and see how soon the direct consequences resulting from his learning disappear in the life of a nation, while the discoveries of a man of science remain productive amid all the shocks of empire. As 1 am in Aberdeen I remember that the learned Dutchman Erasmus was intro- duced to England by the encouragement which he received from Hector Boece, the Principal of King's College in this University. Yet even in the case of Erasmus — who taught Greek at Cambridge and did so much for the revival of classical literature as well as in the promotion of spiritual freedom — how little has civilisation to ascribe to him in comparison with the discoveries of two other Cambridge men, Newton and Cavendish. The discoveries of Newton will influence the destinies of mankind to the end of the world. "When he established the laws by which the motions of .the great masses of matter in the universe are governed, he con- ferred an incalculable benefit upon the intellectual development of the human race. No gi-eat discovery flashes upon the world at once, and therefore Pope's lines on Newton are only a poetic fancy : — Nature and Nature'.s laws laj' hid in night, God said, ' Let Newton be,' and all was liglit. No doubt the road upon which he travelled had been long in preparation by other men. The exact observations of Tycho Brahe, coupled with the discoveries of Copernicus, Kepler, and Galileo, had already broken down the authority of Aristotle and weakened that of the Church. But though the conceptions of the universe were thus broadened, mankind had not yet rid themselves of the idea that the powers of the universe were still regulated by spirits or special providences. Even Kepler moved the planets by spirits, and it took some time to knock these celestial steers- men on the head. Descartes, who really did so much by his writings to force the conclusion that the planetary movements should be dealt with as an ordinary problem in mechanics, looked upon the universe as a machine, the wheels of which were kept in motion by the unceasing exercise of a divine power. Yet such theories were only an attempt to regulate the universe by celestial intelligences like our own, and by standards within our reach. It required the discovery of an all-pervading law, universal thi-oughout all space, to enlarge the thoughts of men, and one which, while it widened the conceptions of the universe, reduced the earth and solar system to true dimensions. It is by the investigation of the finite on all sides that we obtain a higher conception of the infinite — Willst du ins TJnendliche sclireiten, Geh nur im Endlichen nach alien Seiten. Ecclesiastical authority had been already undermined by earnest inquirers such as Wycliffe and Huss before Luther shook the pillars of the Vatican. 28 REPORT — 1885. They were removers of abuses, but were confined within the circles of their own beliefs. Newton's discovery cast men's minds into an entirely new mould, and levelled many barriers to human progress. This intel- lectual result was vastly more important than the practical advantages of the discovery. It is true that navigation and commei'ce mightily benefited by oui- better knowledge of the motions of the heavenly bodies. Still, these benefits to humanity are incomparably less in the history of progress than the expansion of the human intellect which followed the withdrawal of the cramps that confined it. Truth was now able to discard authority, and marched forward without hindrance. Before this point was reached Brnno had been burned, Gralileo had abjured, and both Copernicus and Descartes had kept back their writings for fear of offend- ing the Church. The recent acceptance of evolution in biology has had a like effect in producing a far profounder intellectual change in human thought than any mere impulse of industrial development. Already its application to sociology and education is recognised, but that is of less import to human progress than the broadening of our views of Nature. Abstract discovery in science is then the true foundation upon which the superstructure of modern civilisation is built ; and the man who would take part in it should study science, and, if he can, advance it for its own sake and not for its applications. Ignorance may walk in the path lighted by advancing knowledge, but she is unable to follow when science passes her; for, like the foolish virgin, she has no oil in her lamp. An established truth in science is like the constitution of an atom in matter — something so fixed in the order of things that it has become independent of further dangers in the struggle for existence. The sum of such truths forms the intellectual ti-easure which descends to each generation in hereditary succession. Though the discoverer of a new truth is a benefactor to humanity, he can give little to futurity in com- parison with the wealth of knowledge which he inherited from the past. We, in our generation, should appreciate and use our great possessions — For me j-our tributary stores combine, Creation's heir ; the world, the world is mine. EEPOETS ox THE STATE OF SCIENCE. EEPORTS ON THE STATE OF SCIENCE. Report of the Committee, consisting of Professor G. Carey Foster, Sir W. Thomson, Professor Ayrtox, Professor J. Perry, Pro- fessor W. Gr. Adams, Lord Kayleigh, Dr. 0, J. Lodge, Dr. John HoPKiNSON, Dr, A. ]Muirhead, ]Mr. W. H. Preece, Mr. H. Taylor, Professor Everett, Professor Schuster, Dr. J. A. Fleming, Pro- fessor Gr. F. Fitzgerald, ]Mr. R. T. Gla/ebrook {Secretary), Pro- fessor Chrystal, ]Mr. H. Tomlixson, and Professor W. Garnett, appointed for the pmrpose of constructing and issuing practical Standards for use in Electrical Measurements. The Committee report tliat during the year the standards of resistance, ia terms of the legal ohm referred to in the last Report, have been con- structed, and their values determined ia accordance with the resolution adopted on June 25, 1884. The one-ohm standards were generally referred to the original B.A. units of the Association by combining in multiple arc with the standard one of the 100 B.A. units, and determining by Carey Foster's method the difference between the combination and a B.A. unit, and then assuming', in accordance with the resolution, that 1 B.A. unit ^ '9889 legal ohm. The following values were thus found for the two standards. The temperatures were taken by a thermometer graduated to tenths of a degree centigrade, which had been compared with the Kew standards. Resistance Coil, Elliott, No. 139, ^ 100. Date Temperature Resistance Nov. 24, 1884 ,. 26, „ ,, 27, „ .. 28, „ Dec. 5, „ 12 July 30,' 188.5 ,. 28, „ ll°-4 11°-G 12°-9 13°-5 13°-5 15°3 n°-2 18°^l •99878 •99890 •99916 •99930 •99931 •99979 1^00027 1-OOOGl Mean value . Temperature cosfEcient ■999515, at 14°^1 C. •000271 32 EEPORT — 1885. Resistance Coil, Elliott, No. 140, ^ 101. Date Temperature Resistance Nov. 24, 1884 . ll°-4 •99813 ,. 25, „ ll°-5 -99815 Dec. 2, „ 12°-8 •99847 Nov. 27, „ 12°-9 •99851 Dec. 5, „ 18°-4 •99865 „ 12, „ 15°-4 •99917 July .30, 1885 17°-2 -99961 „ 29. „ 18=-0 •99983 Mean value . Temperature coefficient •998815, at 14°-1 C. •000259 The ten-olim standards were tlien compared with the one-ohm by means of the arrangement suggested by Lord Rayleigh, and described in the Report for 1883, and from these values were obtained for tlie coils of higher resistance. The results are contained below. No. of Coil Resistance Temperature No. 141, ;^ No. 102 10-00103 lG°-7 No. 142, ;^ No. 103 10-00169 16°-75 No. 143, ;^No. 104 99-9977 16°-05 No. 144, "^ No. 105 100-0108 16°05 No. 145, "^ No. 106 1,000-306 17°-4 No. 146, ;^ No. 107 1,000-276 17°-4 No. 147, ^ No. 108 10,002-4 17°-35 No. 148, ^ No. 109 10,002-4 17°-35 These experiments were carried out at the Cavendish Laboratory by the Secretary and Mr. H. Wilsou, of St. John's College. At the request of M. Mascart, the Secretary compared with the legal ohms of the Association three mercury copies of a legal ohm, constructed by M. J. R. Benolt, of Paris. A detailed account of these experiments was laid before the Physical Society.' The values found are given below. No. of Tubes Value found bv M. J. R. Bcnoit Value found bv K. T. G. Diff 37 38 39 1-00045 1-00066 •99954 -99990 1-00011 -99917 •00055 ■00055 ■00037 Moan 1-00022 •99972 •00049 ' ridl. Mil//. Oct. 1885. ON STANDARDS FOR USE IN ELECTRICAL MEASURE5i'ENTS. 33 The work of testing resistance-coils has been continued, and a table of the values found for the various coils examined is given. British Association Units. No. of Coil Eesistance in B.A. Units Temperature Elliott, No. 122 f $^ No. 61 1 Elliott, No. 58 10-0163 100017 9-9885 9-9834 19°-8 15°-2 10' -5 14°05 Legal Ohms. No. of Coil Jlesistance in Legal Ohms Temperature "^ No. 150 ^ No. 151 Elliott, 149, '^ No. 152 Elliott, 136, '^ No. 153 :^ No. 154 •99895 •99974 •99912 •99977 100032 ll°-7 13°-9 12°-5 12°-4 17°-3 The Committee hope that arrangements may be made for issuing standards of electro-motive force and constructing standards of capacit3\ In conclusion, they would ask to be reappointed, with the addition of the names of Professor J. J. Thomson and Mr. W. N. Shaw, with the re- newal of the unexpended grant of 60/. Report of the Committee, consisting of Professors A. Johnson (Secretary), J. Gr. MacGtREGOR, J. B. Cherriman, H. T. Bovey, and Mr. C. Carpmael, appointed for the purpose of promoting Tidal Observations in Canada. The Committee have represented to the Canadian Government the importance of publishing tide-tables for Canadian waters, and the neces- sity for this purpose of establishing stations for continuous tidal observa- tions, recommending that the observations be subsequently reduced by the methods of the British Association. They have pointed to the example of the United States Government, which has provided tide-tables for both the Atlantic and Pacific coasts. In urging the practical side of the question they have more especially referred to the tide-tables for British and Irish ports published by the Admiralty, which give the rate and set of the tidal currents in the waters surrounding the British islands ; and they have drawn attention to the heavy annual losses caused by ignorance of these currents in Canadian waters, as shown by the wreck list. 1885. D 34 EEPORT — 1885. In ordei' to strengthen their representation from this point of view, they deemed it well to get the opinions of Boards of Trade and ship- owners and shipmasters. On inquiry it appeared that the Montreal Board of Trade were at the very time considering the qnestion, which had been brought independently before them. On learning the object of the Committee they gave it their most hearty support, and addressed a strong memorial on the subject to the Dominion Government. The Boards of Trade of the other chief ports of the Dominion also sent similar memorials. The shipowners and masters of ships, to whom application was made, were practically nnanimons in their testimony as to the pressing need for knowledge on the subject. The representations of your Committee were made through the Minister of Marine, with whom an interview was obtained, at which a memorial was submitted. Copies of the answers of the shipmasters (a large number of which had been received) were submitted at the same time. Full explanations, in reply to the inquiries of the Minister, were given, more especially on practical points connected with the proposed observations at fixed stations and the reductions, for which your Com- mittee are largely indebted to a corresponding committee appointed by the Council, consisting of the Right Hon. Sir Lyon Playfair, Professor J. Couch Adams, Sir William Thomson, and Professor Darwin. During the session of Parliament the Royal Society of Canada also addressed petitions to the Governor-General and the two Houses of Parliament, strongly urging the need of tidal observations. The reply of the Minister of Marine stated that, owing to the large outlay on the Georgian Bay Survey, and on the expedition to Hudson's Bay during the past summer (18S5), the Government did not propose to take action in the matter of tidal observations at present. This un- favourable answer, it will be observed, is made to depend on a temporary financial condition, and your Committee have reason to believe that if the financial ]irospects improve by next session of Pai-liament, the Govern- ment will take the matter into earnest consideration ; they therefore suggest that the Committee be reappointed. Fifth Report of the Committee, consisting of j\Ir. John jNIurray (Secretary), Professor Schuster, Professor Sir William Thomsox, Professor Sir H. E. KoscoE, Professor A. S. Herschel, Captain W. DE W. Abxey, Professor Bonney, Mr. E. H. Scott, and Dr. J. H. Gladstone, appointed for the purpose of investigating the practicability of collecting and identifying Meteoric Dust, and of considering the question of undertaking regular observations in various localities. The Secretary reported that collecting apparatus had been sent to various oceanic islands, and that a report would be prepared by next year on the specimens received. ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 35 Third Report of the Gommittee, connsting of Professors G. H. Darwin and J. C. Adams, for the Harmonic Analysis of Tidal Observations. Drawn up by Professor G. H. Darwin. I. Record of Work during the past Year. The edition of the compntafcion forms referred to in the second report is now completed, and copies ai'e on sale with the Cambridge Scientific Instrument Company, St. Tibbs' Row, Cambridge, at the price of 2s. GtZ. each. Some copies of the first report, in which the theory and use of those forms are explained, are also on sale at the same price. A few copies of the computation forms have been sent to the librarians of some of the principal Scientific Academies of Europe and America.* In South Africa, Mr. Gill, at the Cape, and Mr. Neison, at Natal, are now engaged in reducing observations with forms supplied from this edition. A memorial has been addressed to the Government of the Dominion of Canada, urging the desirability of systematic tidal observation, and the publication of tide-tables for the Canadian coasts. There seems to be good hope that a number of tide-gauges will shortly be set up on the Atlantic and Pacific coasts, and in the Gulf of the St. Lawrence. The observations will probably be reduced according to the methods of the British Association, and the predictions made with the instrument of the Indian Government. Major Baird has completed the reduction of all the tidal results obtained at the Indian stations to the standard form proposed in the Report of 1883, and Mr. Roberts has similarly reduced a few results read before the Association by Sir William Thomson and Captain Evans in 1878. All these are now being published in the ' Proceedings of the Royal Society,' in a jmper by Major Baird and myself. A large number of tidal results have been obtained by the United States Coast Survey, and reduced under the superintendence of Professor Ferrel. Although the method pursued by him has been slightly different from that of the British Association, it appears that the American results should be comparable with those at the Indian and European ports. Professor Ferrel has given an assurance that this is the case ; nevertheless, there appears to be strong internal evidence that, at some of the ports, some of the phases should be altered by 180°. The doubt thus raised will probably be removed, and the paper before the Royal Society will afford a table of reference for all — or nearly all — the results of the harmonic method up to the date of its publication. The manual of tidal observation promised by Major Baird is now com- pleted, and will be published shortly. This work will explain fully all the practical difficulties likely to be encountered in the choice of a station for a tide-gauge, and in the erection and working of the instrument. Major Baird's great experience in India, and the success with which the operations of which he has had charge have been carried out, render his ' Namely, the Koyal Societies of London and Edinburgh, the Royal Irish Aca- demy, the Academies of Paris, Berlin, and Vienna, the United Coast Survey, and the Cambridge Philosophical Society. D2 36 REPOKT — 1885. advice of great value for tlie prosecution of tidal observation in other conntries. The work also explains the method of measuring the tide diaorams, entering the figures in the computation forms, and the sub- sequent numerical operations. II. Certain Factors and Angles used in the Reduction of Tidal Observations. In completing the reduction of the results of harmonic analysis to the standard form, a number of angles and factors are required which de- pend on the longitude of the moon's node. Tables of these angles and factors have been computed under the superintendence of Major Baird.' It may happen, however, that the tables are inaccessible to the computer, and the computation from the full formulae might be somewhat laborious. It happens that the angles r, £, v', 2v" (the meanings of which are ex- plained in the Report of 1883) are all expressible in the form A sin iV+B sin 2iV+C sin 3i^+ , where N is the longitude of the moon's node, and that the coefiBcients diminish with such rapidity that the first two terms are probably sufficient for all practical purposes. Also the several factors f are reducible to the form A + B cos N+G cos 2^+ . . . . , and three terms are practically sufficient. I have obtained the approximate formulze given below in this form. The rigorous results having been tabulated, it appeared easier to work from them instead of from analytical expressions in terms of the longitude o£ the moon's node. I find, then, the following results : — Schedule I. Approximate Formula; for Angles. .' =12°-9 sin A^-l°-3 sin 2N, I =,'-l°-07 sin N, (forK,) v' =z8°-8sinN-0°-6sm2N, (for Ka) 2»'"=17°-8 sin N- 0°-5 sin 2^^, Also A =16°-51 + 3°-44 cos ^-0°-19 cos 2N, and A,=16°-36. For the meanings of A and A^ the reader must refer to Part IV. Approximate Formulce for Factors f. For Mj and other tides, f = — cos^ U ^1-0003 _ -0373 cos iV-l--0002 cos 2N. cos'' ^o) cos* -^i For 0, f= . ^'" -^,^"^' ^^^ , =1-0088 + 1886 cos J^--0146 cos 2A^. sm w cos'^ io) cos* ^i ForK2 f= 1-0243 + -2847 cos A'+ -0080 cos 2Jv^. ForKi f=l-0060 + -1156 cos Jv^- -0088 cos 2iVr. ForMf . . f= . /'''' ^, , =1-0429 + -4135 cos .^-•0040 cos 2^. sm'' <i> cos* ^4 • Some of these are given in the Report of 1883. ON THE HARMONIC ANALTSIS OF TIDAL OBSERVATIONS. 37 For Mm, (1— Isin^w) (1— fsin^i) f= ^7~K^]f \ ■ ., .. =l-0000--r299 cos N+ -0013 cos 2N. Even if all the terms in 2N were omitted, the approximations might be good enough for all practical purjioses. III. On the Periods chosen for Harmonic Analysis in the Computation Forms. Before proceeding to the subject of this section, it may be remarked that it is unfortunate that the days of the year in the computation forms should have been numbered from unity upwards, instead of from zero, as in the case of the hours. It would have been preferable that the first entry should have been numbered Day 0, Hour 0, instead of Day 1, Hour 0. This may be rectified with advantage if ever a new issue of the forms is required, but the existing notation is adhered to in this section. The computation form for each tide consists of pages for entry of the hourly tide-heights, in which the entries are grouped according to rules appropriate to that tide. The forms terminate with a broken number of hours. This, as we shall now show, is erroneous, although this error may not be of much practical importance. In § 9 of the Report for 1883 the following passage occurs : — ' The elimination of the effects of the other tides may be improved by choosing the period for analysis not exactly equal to one year. For suppose that the expression for the height of water is Ai cos ?!i< + Bi sin jii^ + Ao cos 7i2i-fB2 sin «2^ • • • (^1) * where 11.2 is nearly equal to «i, and that we wish to eliminate the n2-tide, so as to be left only with the «i-tide. ' Now, tbis expression is equal to {A,+A2Coa (?ii— ?i2)«^ — Bo sin («i — «-2)^} cos n^t) + [Bi+A2 sin (71,— «2)i + B2 COS ('h— 7J2)0 sin «ii] * ' That is to say, we may regard the tide as oscillating with a speed tiy, but with slowly varying range.' Although this is thus far correct, yet the subsequent justification of the plan according to which the computation forms have been compiled is wrong. In the column appertaining to any hour in the form we have n^t a multiple of 15°, if n^ be a diurnal, and of 30°, if 71^ be a semidiurnal tide. Consider the column headed 'phours ' ; then nit=15° p for diurnals, and 30°_p for semidiurnals. Hence (62), quoted above, shows us that, for diurnal tides, the sum of all the entries (of which suppose there ai'e 2) in the column numbered y-hours, is 38 EEPORT — 1885. cos lb°p{A^q + AJcoa(',H-n.^^ + co3[(in,-7io)(^^^ + ^J] + cos[0h-«2)('2^ + i^')]+ . . ."]+P,[&c.]}+sml5°p{&c.} (a) And for semidiurnal tides the arguments of all the cii-cnlar functions in (a) are to be doubled. Now, we want to choose such a number of terms that the series by which A2 and Bo are multiplied may vanish. This is the case if the series is exactly re-entrant, and is nearly the case if nearly re-entrant. The condition is exactly satisfied for diurnal tides, if {ni—7i2)q — =27rr, where r is either a positive or negative integer. And for semidiurnal tides, if (?i, — ^2)2 — =27n'. That is to say, (^^ni—n2)q—nir, for diurnal tides, or (h, — H2)2=5'^i'*> for semidiurnal tides. It is not worth while attempting to eliminate the effect of the semi- diurnal tides on the diurnal tides, and vice versa, because we cannot be more than a fraction of a day out, and on account of the incommensurability of the speeds we cannot help being wrong to that amount. S Series. Now suppose we are analysing for the Sj tide, and wish to minimise the effect of the M2 tide. Then n,=2(y— »?)=2 xl5° per hour, 712 = 2(7-0-), 9;i-?!2=2(<r-'?)=l°0]58958 per hour. The equation is l°-01589582=15°r. If r=25, 2=369-13. Thus 25 periods of 2((7 — ??) is 369-13 mean solar days. It follows, therefore, that we must sum the series over 369 days in order to be as near right as possible. Now this is equally true of all the columns, and each should have 369 entries. Hence, in order to have 369 entries in each column, the present 83 computation form should have the last three entries cut off. The divisors are to be, of course, changed accordingly. M Series. Now consider that we are analysing for Mg, and wish to minimise the effect of the S., tide. Hence ON THE HARMONIC ANALYSIS OF TIDAL OBSEEYATIONS. 39 n,=2(7 -,t)=2 X 14°-4920521 per hour, n2 = 2(y-r,), «,-,i2=_l°-0158958 per Lour. Hence, taking r negative, the equation is l°-01589582=14°-4920521r. If 5-25, 2=356-63. Thus 25 periods of 2(r7 — rj) is 356'63 of mean lunar time. It follows, therefore, that we must have 857 entries in each column. Thus the M, computation forni should have the row numbered 357 complete, adding 9 more entries. There are no ' changes ' amongst these 9 entries. The divisors are to be modified accordingly, here and in all subsequent cases. K Series. To minimise the effect of Mg on K,, we have ni = 2y=2 xl5°-041068G per hour, «2 = 2(y-0, ni-«2=2(T-,,) = l°-0158958 per hour. l°-0158958g=15°-0410C86r. If r=25, 2=37014. Hence we should complete the row numbered 370. The last 3 entries of the existing tables are to be cut off. To minimise the effect of O on K,, we have w, = y=15°-0410686 per hour, 112=7 -2<r, w,-H2=2<T=l°-0980330 per honr. l°-09803302=15°-0410686r. If r=27, 2=369-85. Thus 2=370 again gives the best result, and confirms the conclusion from the above. The N Series. Here 7ii=2y-3<7 + -ir=2 xl4°-2198648 per hour. To minimise the effect of M2, «2=2y — 2(r, ni— ??2=(<T-'57)=-0°-5443747 per hour, 0-54437472=14°-2198648r. If r=13, 2=339-58. Hence we should complete the row numbered 340. There is no justification for the alternative offered in the computation forms of continuing the entries up to 369'' 3'^ of mean solar time. The L Series. Here ni = 2y-(T- ^=2 xl4°-7642394 per hour. 40 REroKT — 1885. To minimise tlie effect of M2, )i,2^2y — 2(T, «j —n.2 = (T — '!!r=0°'5i4>S74i7 per hour. 0'54437472=14°7642394r. If, .-=13, f^=352-58. Hence we should complete the row numbered 353. There is no justification for the alternative offered in the computa- tion forms of continuing the entries up to 369*^ 3*^ of mean solar time. The r Series. Hero 92,=27-3a-'sr + 2;j=2 xl4°-2562915 per hoar. To minimise the effect of M.,, ^!2 = 27 — 2(7, n -i/2=-o--w+2>j=-0°-4715211 per hour. 1 —"2 0-471o211';=14-256291.5)-. Ifr=ll, 2=332-6, Hence we should complete the row numbered 333. There is no justification for the alternative offered in the computation forms of continuinp: the cnti ies up to 369'' 3^ of mean solar time. The X Series. Here ni=27-a + 'z^-2;/ = 2 xl4°7278127 per hour. To minimise the effect of Mj, n,=2y-2(T, «,,— 772=(T + «r — 2>;=0°-4715211 per hour. 0-471521l2=14-7278127r. If r = ll, 2=343-58. Hence we should complete the row numbered 344. There is no justification for the alternative offered in the computation forms of continuing the entries up to 369*^ 3*^ of mean solar time. The 2N Series. Here w,=2y-4ff + 2'ar=2 xl3°-9476774 per hour. To minimise the effect of Mj, ^2=27 — 2t, ni-n2=-2(o--'nT)=l°-0887494 per hour. l-08874942=13-9476774)-. Ifr=26, 2=333-08. Hence we must complete the row numbered 333. The T Series. Here 7ii=27-3»;=2 xl4°-9794657 per hour. To minimise the effect of M2, n^=2y-2rr, ni-«2=2T-3T = 0°-9748272 per hour. 0-97482722=14-9794657r. Ifr=24, 3=368-79. ON THE HAiniONIC ANALYSIS OF TIDAL OBSERVATIONS. 41 Hence we must complete the row numbered 369. The'R Series. Here wi=2y-»;=2 x 15°0205343 per hour. To minimise the effect of Mj, no=2r-2a, 71, — «2=2ff — ii=l°"0569644 per hour. l-0569644(7=15-0205343)-. If r=25, 2=355-28, and r=2G, g=369-49. Hence we should either complete the row numbered 355 or that numbered 369. The 2MS Series. Here ni = 2y-4(T + 2»;=2 xl3°-9841042 per hour. To minimise the effect of M2, «2=2y-2^, M, -7i2= -2(<T-7;) = -1°-0158958 per hour. l'0158958r/=13-9841042r. If r=24, 2=330-37, and ?-=25, 2=044-13. Hence we should either complete the row numbered 330 or that numbered 344. The 2SM Series. Here Wi=2y + 2(r-4rj=2 xl5°-5079479 per hour. To minimise the effect of M,, «2=2y-2^, «,-n2=4(ff— r?)=2°-0317916 per hour. 2-03179162=15-5079479)-. If r=48, 2=366-37. Hence we should complete the row numbered 366. The Series. Hero . n,=y-2(r=13°-9430356 per hour. To minimise the effect of Kj, ni-n2=-2ff=-l°-0980330 per hour. l-09803302=13-9430356>-. If r=27, 2=342-85. Hence we should complete the row numbered 343, cutting off the last three entries in the present forms. The P Series. Here «i=y-2,,=14°-9589314 per hour. It is open to question whether it is best to minimise the effect of K, or of O. 42 EEroRT — 1885. For Ki take '>H=y, ,ij-,i2=-2»j=-0°-0821372 per hour. 0-0821372<7=14-9589314r. Ifr=2, 2=364-24. Hence we should complete the row numbered 364. For O, take ^2=7 — 2(t, ,;.,_7i2=^2((T— 7j)=l°'0158958 per hour. l-01589582=14-9589314r. Ifr=25, 2=368-12. Hence we should complete the row numbered 368. It is better to abide by this, for in the former case n^ —n^ varies very slowly ; and we may be satisfied that on stopping with row 368 the effects of and Kj will both be adequately eliminated. The J Series. Here 7ii = y + (r— 'ct=15°-5854433 per hour. To minimise the effect of Kj, «2=r, Wj— n2='7 — 'nr=0°'5443747 per hour. 0-5443747(7=15-5854433*-. If r=12, 2=343-56, and r=13, 2 = 37219. To minimise the effect of O, Wo=:y — 2(r, «j— n2=3(T-c7=l°-6424077 per hour. l-64240772=15-5854433r. If r=36, 2=341-6, and r=39, 2=370-09. Since in the latter case n^ — Ur^ varies three times as fast as in the former, it will be better to abide by this, and stop either with the row numbered 342 or that numbered 370. The Q Series. Here «i=y-3(r + '=7=13°-3986609 per hour. To minimise the effect of K,, ?i2=y, ,ii_,j2=-(3a-w) = -l°-6424077 per hour. l-64240772=13-3986609r. If r =38, 2 = 310-00. To minimise the effect of O, 7i2=y — 2(T, n, — n2= — (ff — 'nr) = — 0°-5443747 per hour. 0-54437472=13-3986609r. If r=12, 2=307-36. Since in the former case ni—V2 varies about three times as fast as in ON THE HAKMONIC ANALYSIS OF TIDAL OBSERVATIONS. 43 the latter, it will be better to abide by the former, and stop with the row numbered 310. With regard to the quaterdiurnal and terdiurnal tides, it does not signify where we stop ; but it seems more reasonable to stop with the exact year of 365 mean solar days. These tides are called MS, MN, MK, 2MK. Schedule II. Periods over which the Harmonic Analysis should extend. Initial of series Number of day and hour of last entry in special time Period elapsino; from O"* of spe- cial day 1 to 23'' of last special day in mean solar hours s 369-1 23^ 368'' 23h M 357 23 369 11 K 370 23 368 23 N 340 23 358 15 L 353 23 358 14 V 333 23 350 8 X 344 23 350 8 2N 333 23 358 2 T 369 23 369 11 E 355 23 or 370 23 354 11 or 369 11 2MS 330 23 or 344 23 353 22 or 368 23 2SM 366 23 353 23 343 23 368 23 P 368 23 368 23 J 342 23 or 370 23 329 3 or o56 1 Q 310 23 347 In the second column the numbers are given to the nearest mean solar hour. 44 EEroET — 1885. IV. A Comparison of the Haemonic Treatment of Tidal Observations WITH THE Older Methods. § 1. On the Mefliod of Computing Tide-tables. There is nothing in the harmonic reduction of tidal observations which necessitates recourse to mechanical prediction of the tides. It may happen that it is desirable to produce a tide-table by arithmetical processes, and that the computers prefer to use the older methods of corrections, or it may be desired to obtain the tidal constants in the har- monic notation from older observations. For either of these purposes it is necessary to show how the liarmonically expressed results may be converted into the older form, so that the constants for the fortnightly inequality in time and height, and the corrections for parallax and declination, may be obtained from those of the harmonic analysis, and conversely. In the following sections I propose, therefore, first to reduce the har- monic presentment of the resultant tide into the synthetic form, where we have a single harmonic term depending on the local mean solar time of moon's transit, and on corrections depending on the R.A., declination, and parallax of the perturbing bodies. Subsequently it will be shown how a synthesis may bo carried out more simply by retaining the mean longitudes and elements of the orbits. § 2. Notation for Mean Heights and llefardations derived from the Harmonic Method. The notation of the Report of 1883 is adopted ; and I shall carry the approximation to about the same degree as has been adopted by the older writers. Closer approximation ma}', of course, be easily obtained. In the Report of 1883 the mean height ' of a tide is denoted by H, and the retardation or lag by k. In the present note it will be necessary to refer to several of the H's and /.'s at the same time, and therefore it is expedient to introduce the following notation : — Schedule III. Initial of Mean height Retardation Initial of Mean height Retardation tide (H) («) tide (H) i'^) Ma M 2/x L L 2\ S2 S 2i: T T 2C Lunar K, K" 2/v- R B 24 Solar K2 K!' 2/.- M' /-' K, K2 2^- P S' <:' N N 2r 1 K, ^1 '-"i In this schedule we assume T and R (of speeds 2y — 3ij and 27 — 77) to have the same lag as S2 ; and we use v in a new sense, the old )■, the ' I use height to denote semi-range. All references to this Report will simply be by the date 1883. ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 45 R.A. of the intersection of the equator with the lanar orbit, being denoted by r^. The initials of each tide are used to denote its height at any time. § 3. Introduction of Sour-angles, Parallaxes, and Declinations. We must now get rid of the elements of the orbit and of the mean longitudes, and introduce hour-angles, declinations, and parallaxes. At the time t let a, ^, xp he 5 'sR.A., and declination, and hour-angle, and n^, ^'^, \p^, © 's R.A., and declination, and hour-angle. Let Z be 5 's longitude in her orbit measured from ' the intersection,' and a — I'o (I'o being the r of 1883) be D 's R.A. measured from the intersection. The annexed figure exhibits the relation of the several angles to one another. The spherical triangle affords the relations tan (fi — ro)^cos/tanZ, sin o=sin7sinZ .... (1) From the first of (1) we have, approximately, a = ?+r^-tan2iIsin2Z (-2) Now, s — s is the moon's mean longitude measured from J, and s—p is the mean anomaly. Hence, approximately, Z = s— ^-|-2e sin(s— ;)) (3) And therefore, approximately, a = s + »'o — s + 2esin(s— J)) — tan^^/sin 2(s— ^) . . . (J.) Now, t-\-li being the sidereal hour-angle, 4. = <-|-7i-a (5) Therefore, from (4) and (5), f + /i_s-(r„-£)=i//-f2esin(s-p)-tan2iZ"sin2(s-£). . (6) By the second of (1) we have, approximately, cos2c = l — |sin-l4-Jsin2/cos2(s— I) .... (7) Hence, if A be such a declination that cos-A is the mean value of cos^ o, we have cos^A =1— isin^ J ) (8) ^2a, and cos^A^= 1 — ^sin^ From this we have (neglecting terms in sin'* A) the following relations: — cos^ ^1= cos^A, sinlcos^ il= V2sinAcosA, sin^ J= 2sin2 A, cos'* -1^ = cos'- A ^, sinwcos^^w^ -%/2sina) cos w, sin-w=2sin2 A^. 46 REPOET 1885. Thus we may put cos* il cos^ A sin2A\ sin Jcos^ jl sin (o cos^ ^ w CDS'* it sin 2 A^ tanHI=itan2A cos* ^a> COS* ^i COS- A, sin^I _sin2A sin2w(l — o-sin^t) sin'^A/ An approximate formula for A and the ralue of A, are A = 16°-51 + 3°-44cosN-0°-19 cos 2N, A =16°-36 The introduction of A and A^ in place of I and w entails a loss of accuracy, and it is only here made because former writers have followed that plan. It may easily be dispensed with. Now let us write (?) (10) D=cos2(s— i), n=cos(s— p), From (7) and (8), J. cos^ c — cos^ A sm^ A D'=sin2(s-£)' n'=sin (s— p) J-, sine cos? do ffsin^A dt (11) (12) Then, if we write for the ratio of the moon's parallax to her mean paral- lax P, we have P — 1 = ccos(s— j>), and n'=- dP (13) n = -(P-l), - , . n e e{rT — ij) at Hence D, D', IT, IT are functions of declinations and parallaxes. The similar symbols with subscript accents are to apply to the sun. Now (G) may be written by aid of (9) and (11), o[; + 7,_5_(,,^_t)]=2J/ + 4en'-D'tan2A . . . (14) The left-hand side of (14) is the argument of M, (see Sched. B. i. 1883), and from (9) the factor of M., is cos^A/cos^A,. Hence, subtracting the retardation 2ju from (14) we have (Mo)=-^^3/cos[(2-^H-4en'-D'tan2A)-2/x], ' cos-A; expanding approximately, (Mo)=^-^4^3fcos2(>i.-A.) cos^'A^ cos-A cos"^A, sin^A cos^A, n'43fesin2(4/-/i) D'3Isin2(J.-^) (ir.) We shall see later that the two latter terms of (15) are nearly annulled by terms arising from other tides, and as in the case of the sun the rates of change of parallax and declination are small, we may write by symmetry, ^ (So) = Scos2(v/.,-0 (IG) ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 47 In all the smaller tides we may write A general formula of transformation will be required below. Thus, if cos2a'^X, sin2.ii=X', :^ -sin2(;/.-^) . (17) C0S2(ct — yti) y-r r/ V y The lunar Kn tide. From Sched. B. i., 1883, we have Lunar K2=^,-^'°!^Ji:"cos2r^ + 7i-ro-'^-] sin-(.i(l— l^sin-^t) o J ''"^Z"cos2[v;/+(s-0-'^-]- sm Applying (17) with X=D, X'=D', a=/.-, and taking the lower sign, In the case of the sun we neglect the terms in D', for the same reasons as were assigned for the similar neglect in (16), and have Solar Ko=7r/'Z),cos2(4.,-/.) (19) The tide N. From Schedule B. i.. Report 1883, COS'^WCOS'^l ^ V z-/ J ^^'^ (N)=^^^cos2[;^-,.-K«-p)]. Then applying (17) with X=U, X'=n', a = r, and taking the upper sign, bat writing ^t — r instead of j' — ^(, because this tide being slower than M2 suffers less retardation, (N)=^5^^r(n+tan2(^-r)n')cos2(;//-r) The tide L. We shall here omit the small tide of speed 2y — ff + 'nr, by which the true elliptic tide is perturbed. Thus the B in the column of arguments in Sched. B. i., 1883, is neglected, and we have 48 KEPOKT — 1885. Applying (17) with X=n, X'=n', n=\, and taking the lower sign, and changing the Bign of the whole, because of the initial negative sign, (L) = ^^^^Lr(-n-tan2(\-//)n')cos2(v/.-X) COS^-!k/ L n2(+-rtj . (21) 4 I cos2(\— y^t) The sum o/N and L. In order to fuse these terms an approximation will be adopted. The L tide is just as much faster than Mo as N is slower, but the N tideshould be nearly 7 times as great as the L tide; hence the tan2(\-/t) in (21) will be put equal to tan2(^-)0. We then have (N) + (L)=-^r(n + tan2(/.-On')(^cos2(»/.-,')-Lcos2(;/.-\)) J COS -^/L " + n'(A"sec2(/x-.) + Lsec2(\-^))sin2(^-^.)]- J^cos2rJ/->0— Lcos2(>/.-X)=cos2;/.(A^cos2)'-Lcos2\) + sin 2ijt'(W'sin 2i-isin2X). Then writing , o iV'sin2i' — Lsin2\ /^qx JVcos2>'— -Lcos2a BO that £ is nearly equal to r, we have ^ ^^^ ■' cos^A^ cos2£ L J + £!^r(i^sec2(^<-.')+i>8ec2(\-/z))sin2(>^-^)] . (23) cos-'AX J In the symmetrical term for the sun, with approximation as in (16), j ^^^^^ (T) + (R)=(r-ii;)n,cos2(;//-0 (24) This terminates the semidiurnal tides which we are considering; but | before proceeding to collect the results some further transformations must be exhibited. -r^, , • n -n /i tx Let us consider the function D + xB', where x is small. From (12) we see that n • ^ 5 js cns'c— cos'^A 1 2 sine cos cad ^ sin^A (T sin-'A at Hence, if S' be the moon's declination at a time earlier than the time of observation by x/2cr, then ^_^^^,^cosV-cos^_ . sm'^A Hence, in (17), ■n . ^ or ^n' cos^o'— cos^A .^.. D-ftan2(K — w)!* = r-:7\ .... (.^0; ' sm^A when h' is the moon's declination at time tV^-57°-3 tan 2(k-^)/2(7. The period 57°-3 tan2((c-;:x)/2<7 may be called ' the age of the declinational inequality.' ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 49 Again, e [ a — 'cjdt) Hence, if {F — Vjje denotes the valae of (P— l)/e at a time xj(ff — 'sr) earlier than that of observation, then n+an'=l(P'-i). e Hence, in (23), n + tan2(^-r)n'=l(P'-l) (26) where P' is the ratio of the moon's parallax to her mean parallax at a time tV'-'57°-3 tan 2(^-r)/(<7-^). The period 57°-3tan2(/x-r)/(<7-w) may be called ' the age of the parallactic inequality.' In collecting results we shall write the sum M2 + So + K2 + N + L + R + T = ;i2. For reasons explained below we omit terms depending on the rate of change of solar parallax and declination. Then, from (15), (16), (18), (19), (23), (24),' (25), (26), we have h, = ^^ M cos 2(4^ -fi) + S cos 2(4^-0 cos-A^ sin^A, ^' ^ sm^A, ' ^^' * _sjnacosS cl2r K^ _af tan^A,") sin2(;^-^) ffsin^A^ f/^Vcos 2(ic— /x) / , COS^A.T,, T .^COS 2^ — ^003 2/\ r>/ 1 \ + — 2^(P'-1) 5 cos2(4/-£) cos^'A, ecoszt + (P^-l)i?!:iZ^cos 2(;/.,-0 cos- A_ 1 dP f^ ^j._ Nsec2(ft-v) + Lsec2(\-fx) COS- A, (T — tn- dt r41f-^^'^^«^(^-") + ^^""^(^-^)^sin2(^-;,) (27) It may easily be shown, from Schedule B. i., 1883, that in the eqni- librium theory 'it" — If tan2A,=0, and 4M—(N+L)/e=0; hence the terms depending on rates of change of declination and parallax are small. This also shows that we were justified in neglecting the corresponding terms in the case of the sun. Also, since the faster tides are more augmented by kinetic action than the slow ones, the two functions, written above, which vanish in the equilibrium theory are normally actually positive. The formula (27) gives the complete expression for the semidiurnal tide in terms of hour-angles, declinations, and parallaxes, with the constants of the harmonic analysis. We shall now show that with rougher approximation (27) is reducible to a much, simpler form. The retardation of each tide should be approximately a constant, plus 1885, E 50 REroRT — 1885. a term varying -n'ith the speed. Hence all the retardations may be expressed in terms of ^ and /x, and K =[1+ (T, 'hiT-^), a — 1] (T — 7/- It Is clear that i: differs very little from 4, and that ^-At_ 2(M- »)_4-/t a a — •Z3- a — i) The time (^—M-)K<^—v) is called 'the age of the tide,' for reasons explained below, and K — fj, fi — r, not being large angles, do not differ much from these tangents. Hence the ages of the declinational and parallactic inequalities are both approximately equal to the age of the tide. Let ce, then, denote (if— /i)/((T— ?/), the age of the tide. Now, as an approximation, we may suppose that heights of the lunar K2 tide, the N and L tides bear the same ratio to the Mo tide as in the equilibrium theory ; and that the solar Ko, the T and R tides bear the same ratio to the S2 tide as in that theory. Then reverting to the nota- tion with J, w, i in place of A, A„ and writing \ cos iw cos ^1 J we have sin^A T-'/ -pSin^ J^,, cos^A ,- r^fir cos- A -K!'=-^^'\UM, ^""^.^N = leBT, "^^L=iefJ/; sin^ A , cos'' -gl cos- A , " cos- A ^ COS''^u> Also, since (22) may be written tan(2u_20=-^'''"--^'--^t:5^2(X-^ we have, treating fi — >•, X— /^, /' — « as small, approximately, £=;ii-|(;e(ff-'=7)=;t-|(\-r). Also cos^A iVcos 2i' — L cos 2X _ „,, — 2"- 7, -=.3eflf. cos^ A , cos Ze Then reverting to mean longitudes, and substituting the age of tide where required, we find, on neglecting the difference between k and i', For the lunar declinational term, 2 tan2Ufi/cos2[s-a;<T-4'] cos 2(^|y-i;)', For the solar declinational term, 2 tan2 iw S cos 27i cos 2(^p,-0 ; For the lunar parallactic term, 3eflf cos [s— p — cpfff — ot)] cos 2[;^— yn + ^a'((T — •ar)] ; ON THE HAEMOMIC ANALYSIS OF TIDAL OBSEKVATIONS. 51 For the solar parallactic term, 3e,(S' cos (h—pi) cos 2[i!'/ — 4]. Then omitting the terms depending on changes of declination and parallax, we have as an approximation, 7i2=filf fcos 2(>^-^) + 2 tan^iJcos 2[s— a'o— £] cos 2(v/'-0 + 3ecos [s— ^ — f[;(<T — ffl-)] cos 2[-.//— yL( + |((,'((T — -ct)] + ,S [ 1 +2 tan- hw cos 2h + 3e, cos (h-p,) 1 cos 2(4/,- 4) . . (28) In the equilibrium theory we have the lunar semidiurnal tide depend- ing on r~3 cos- c cos 2i//. Now it is obvious that cos^ introduces a factor 1 + 2 tan- ^Icos 2 (s — ^), and i"^ a factor 1 + 3e cos (s—p). Thus, if we could have foreseen the exact disturbance introduced by friction and other causes in the various angles, the formula (28) might have been established at once ; but it seems to have been necessary to have recourse to the complete development ia order to find how the age of the tide will enter. § 4. Reference to Time of Moon's Transit. It has been usual to refer the tide to the time of moon's transit, and we shall now proceed to the transformations necessary to do so. cos- A /cos^ A, goes through its oscillation about the value unity in 19 years ; it is therefore convenient to write for, say, a whole year, c^A_3^ ~ (29) cos-' A / and similarly, N^z=^^'A N cos^ A ; 7- cos^ A COS'' A J "We also observe that K" and Kf, being the lunar and solar parts of the mean K., tide, and their ratio being -464 (Report, 1883), K" = -68303K„ K/'=-3l697K^ .... (30) It will also be seen that in all the terms arising from the sun, exceptincr that in K/', the argument of the cosine is 2(\P,-i;). It will be con°- venient, and sufficiently accurate for all practical purposes, to replace ichy 'C in this solar declinational term Jv'/'. We shall now proceed to refer the tide to the moon's transit at the place of observation. Let a„, h^ be D 's R.A and 's mean longitude at ]) 's transit— say upper transit, for distinctness. Then the local time of transit is given by the vamshing of I, and since xl^=t-\-h-a, it follows that the time-angle ot D s transit (at 15° to the hour) is ci^ — h^. Now let T (mean solar hours) be the interval after transit to which the time-angle t refers ; then, since E2 52 REroKT — 1885. =[(y-'j)^ + «o-/'o] + [/'o + 'r]-['.o + Tr+('~-TV], For the sake of brevity-, put T = (y-<7)T, so that T is r converted to angle at the rate of 14°'49 per hour. Then we have v/.=T-(^;^-.)r (31) Similarly putting o^ for 's R. A. at D 's transit, we have SO that (la Then let ^=«o-a, (32)* So that A is the apparent time of ]) 's transit, reduced to angle at 15° per hour, and we have ;/.,=T + -l+('r-J^)r (33) It is only in the two principal tides that we need regard the changes of R.A. since B 's transit, and in all the smaller terms we may simply put The first pair of terms of (28) now become iLr„cos2[T-(^^-ay-^] + .S'cos2[T + 4+(^^-^p)r-4], and these are equal to lf„ cos 2(T -/.) + ,S cos 2(T 4- ^ - "We may now collect together all the results, and write them in the form of a schedule. * It would be better to put If this bo used the correction (iO) for Q's change of R.A. becomes small. 4 (T — ri •y — a ON THE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 53 /-^ ^•^ /— \ .""s Vr *vj- Kr .\j. u 1 1 1 1 2 ^ ^ a. -^ u -^ a. ^ -t fS 1 + 1 + 1 + 1 1 + 1 1 « H H H H H H EH e-^ EH H 1 '■ ^.^ ^— x_/ v_, 1 (M C-l c^' CM CM <M CM (N (M CM S 00 00 ^fi OQ m _c 03 cc f-i ^ O o O O O o ■ (H Ph o o CO 'S O o 'm u « 00 X X X X X X X X X X ^ -N • a. 1 1 <r C4 CI ^" -4J + ^ 1 iH , ^^ ■n ^ 1 ^ 1 (N 1 c CO a. o -* O o 1 IM . Ci "*■ o CM 6 > 1. t 1 or ^ 1 >< a ■:£ CI O o ) ) CI t/; o o 1 ^ ; 00 1 ■-tf o O 1 CM o o to O o 1 Eh ;§ O 3 ^ -5 1^ . o 2 <^ ^ 1 b ^2 1 O o 1^ CI m c o 'So Cl b I— 1 1 r— 1 l-H ^ 1 b ^ + 1 + H - + 4 + s a • tH o IS • l-t "s a »— • a %. K c < ■ < 1 i i o ^ p^ c a 0) ^3 CQ Ph ' C-H tt-i _o o tw M-l o o o •fH o o (A rt K -*-3 -*J H ^ J CD .£ u c u ? p eS cS o CB c a> P r tj3 bo .S _P fcJ3 : bfi .E ■l ' i o S 'B i g 'ti s_ J3 -a O) 01 ^ s « i -q p- p. ( Q O p p o &4 p. H O A <=> G (=* « G ) <=t 54 REPOET— 1885. Definition of symbols : — a, 5, a„ d, D 's and 's R.A. and declination at moon's transit ; A=a — Uj, apparent time of 1) 's transit at the port. 57°'3 I' 3) 'sdecl.atthetime(generallyearliertliantransit)r ~ — tan2((v — /i). JitT F, P/ the ratio of D 's and 0's parallax to mean paralla,xes. P' the ratio for )) at the time (generally earlier than transit) 7— tan2(/u — )'). r the time elapsed since ]) 's transit in m.s. hours ; T the same time reduced to angle at 14°'49 per hour. A such a declination that cos^ A is the mean value of cos^ o ; A has a lO-yearly pei'iod. A^ such a declination that cos^ A, is the mean value of cos- c,. e, e, eccentricities of lunar and solar orbits ; a the D 's mean motion ; «7 the mean motion of the }) 's perigee. ^^^o^io^COS^ A M IS L cos^A; M, S, K<i, N, L, T, B the mean semi-ranges II of the tide.? of those denominations in the harmonic method. The retardations found by harmonic analysis are 2^i for M,, 2i^ for S.), 2/c for K.>, 2i' for N", 2\ for L, and 2^ for T and R. ' " " . Lastly tan 2e= — ^^ ^ — j ^ 2^ ^q be taken in the same quadrant '' iVcos2)'-ivcos2\ • '■ as 2,'. § 5. Synthesis of the Several Terms. Consider the two principal terms in Schedule IV. M, cos 2(T - ^0 + ,S' cos 2 (T + ^ - . They may be -wi-itten in the form fl'cos2(T-^), where H cos2(n — (j,)=M^ + S cos 2(J. — i+/j), Hsin2(i^-,l>) = Ssm2(A-^ + fi). If we compute f corresponding to the time of moon's transit fi'om the formula tan2(^-^)^ .Ssin2M-^ + ^) 'M, + Scos2(A-(+fiy then (f> reduced to time at the rate of 14°-49 per hour is the interval after moon's transit to liigh water, to a first approximation. The angle + 90°, similarly reduced, gives the low waters before and after the high water, and (j!>-j-180° gives another high water. The high waters and low waters are to be referred to the nearest transit of the moon. The height or depression is given to a first approximation by jff=^/(j\J„2 + g2 + 2iTf„S cos 2 (/x-.^)). OS THE HAKJIONIC ANALYSIS OF TIDAL OBSERVATIONS. 55 This Tariabilitv in the time and height of high water, due to variability of (,'>, is called the fortnightly or semi-menstrual inequality in the height and interval. The period (:^ — /.i) j (cr — i]) is called ' the age of the tide,' because this is the mean period after new and full moon before the occurrence of spring tide. § 6. Corrections. The smaller terms in Schedule IV. may be regarded as inequalities in the principal terms. They are of several types. Consider a term £cos2(T-/3). Then i?cos2CT-/3)=5cos2(/3-0)cos2(T— 0)+5sin2O3-0)sin2(T-0). Hence the addition of such a term to ffco8 2(T — ^) gives us (H+dE) cos 2(T-f-l<p), where cH=B cos 2(ft-(p),2m(p=Bsm2(i3-(l.). . . . (35) Next consider a term C sin 2(T — /^t). Putting /5=yLi + l-, we have 'cR=-Csin2(^i-<p),2Eo<i>=Gcos2(^-(p) . . . (36) Xext consider a term E cos 2(T4 .4 — i^). Putting /3=^—A, we have cE=Ecos2(A-i:+<l>),2Hcf=-Esin2(A-i:+<i,) . . (37) Lastly, consider a term JPsin 2(T + J. — 4). Putting /3=^— J. + |7r, we Lave cE=Fsm2(A-!:+<l>),2El(p=Fcos2(A-C + (p) . . (38) In writing down the corrections we substitute 14'49S^ for c(j), and introduce a factor so that the times may be given in mean solar hours and the angular velocities in degrees per hour. Change of Moon's R.A., Sched. IV. This is of type (36), and gives This correction to the height is very small. Cliancje of Sun's R.A., Sched. IV.* This is of type (38), and gives (89) (40) * "With the value of A suggested in footnote to (.32) {a - da, j dt)r becomes [((p-/i)tr-(<p^a, jdi-nv)] I iy — <r) at high water. This is obviously very small. 56 REPORT — 1885. Moon's Declination, Sclied. IV. This is of type (35), and gives oif=^^5^i^^^^-683Ji2Cos2(^— .ji) sin'' A/ .^^-^^.gj,j,cos^a^-cos2_A sin^ Aj Sun's Declination, Sclied. IV. This is of type (37), and gives •6835 sin 2 (».— </.) (41) cH=^^^lIlZ^2!l^ -317 K2Cos2(A-( + <)>) ' 3f = -lh-977^5^!A:i^£?!^' -.317 ^ sin 2(A-i: + (p) sin''' A, M (42) Change of Moon's Declination, Sched. IV. This is of type (36), and gives SH='^^^l^ da 7 -683 K, Mts^n^A,) sin 2(;.-^)) ffsm^^, dt\cos2{t:-fi) 'J ^^ [(4.3 sin ? cos 2 cU f •683/1, ^ ' U= - P-977- (tH sin^ A Moon's Parallax, Sched. IV. This is of type (35), and gives , dt \co92{k-ii) 7 ^^ ^') cB={p'^iy^ N„ cos 2t' — L. cos 2\ e cos 2£ cos 2(£ — 0) t<=lh-977(P^-l)^'° "°" ^'-^° ^"" '^^ sin 2(£-<^) i/e cos 2£ Sun's Parallax, Sched. IV. This is of type (37), and gives afl"=(P,-l)^^ cos2(4-4+f)' ct= -lh-977(P,-I)^^ sin 2(^-C + «/') Change of Moon's Parallax, Sched. IV. This is of type (36), and gives (44) (45) m=^^ ^f414- ^°^"^^<^-") + ^°^""^^^-^) Uin2(u-ri,)l 1--977 dP^^^^^_ N^sec2(^-r) + L^.ec2(X-,) ^ ' {a—'m)H dt\ e J J H= (46) The lunar corrections involving sines are small compared with those involving cosines. To evaluate these corrections -we must compute r from f reduced to time at 14°'49 per hour. In the right ascenaionalterms, da/dt and a are to be expressed in degrees per hour, da/dt is the hourly change of ))'s H.A. at time of B 's transit, and dajdt is the hourly change of © 's R.A. at time of D 'b transit. ON TUE HARMONIC ANALYSIS OF TIDAL OBSERVATIONS. 57 Similarly, dcjdt is to be expressed in degrees, if a be in degrees. c', P' can be found for the antecedent moments, 57'''3 tan 2(k- — ^()/2o-, and 57°'3 tan 2(/i — i')/(t — ■or), before the time t. § 7. The Diurnal Tides. I shall not consider these tides so completely as the semidiurnal ones, although the method indicated would serve for an accurate discussion, if it be desired to make one. The important diurnal tides are Ki, 0, P. From Schedule B ii., 1883, we have sinlcosHI M'cos [f + 7.-,.,-2(.-0 + iU-//]. sm w cos-' ^w cos'' ^^ By (9) the coefficient is sin 2^ /sin 2^„ and we shall put, as in the case of the semidiurnal tides, bin ZA^ Then, since t + h-=-^ + a, (0)=J/o' cos [4'+(a + ''o)-2(s-0+i'^-A''] =MJ cos ii, for brevity {'^7) Again, from Schedule C, 1883, (P) = ,S'' cos [i-Zi + K-;"] ; Then let x=2(s-/0 + 'o-2^-4' + m'> and we have (?) = «' cos (il + x) (48) Whence (0) + (P) = [lfo' + <S' cos xl cos a-S' sin x sin fi. If we pnt, E' cos {i^'-<i>')=MJ + S' cos X H'sin (^'-.^')='S'Binx. (0) + (P)=fi' cos (O + m'-^') =ir'cos[>/. + («->0-2(s-^)+i7r-f] . (49) Where R'=s/ {ilA'2 + 6"2 + IM^S' cos xl and tan (a'-d,')= ^l^^'^J^ — '^^ ' ^ 34' + /S"cosx (50) The rate of increase of the angle x is twice the difierence of the mean motions of the moon and sun, but it would be more correct to substitute for s and li the true longitudes of the bodies. It follows from (50) that ^' has a fortnightly inequality like that of <l>. \p is very nearly equal to T, and where the diurnal tide is not very large we may with sufficient approximation put (a-rj-2(s-0=-(s-,0. So that with fair approximation (0) + (P)=fl'cos[T-(s-0 + |7r-^'] . . . (51) 58 iiErouT — 1885. The synthesis of the two parts of the Kj tide has been performed in the harmonic method (Report, 1883), and we have (K,) = fi7iri cos (t + h—y' — hTr — i:^). Then, writing iJ{i=K„, we have (K,)=7v„ cos (T + a-.''-i7r-/.i) .... (5-2) We have next to consider what corrections to the time and height of high and low water are necessary on account of these diurnal tides. If we have a function A=I7 + B'cos2(T-./)) + B"iCOs(«T-/3), where n is nearly equal to unity, and H^ is small compared with H; its maxima and minima are determined by sin 2(T-f/>)= -^- sin (nT -/3). If T=To be the approximate time of maximum, and To + oTq the true time, then, since the mean lunar dayis24"84 hours, and the quotient when this is divided by Stt is 0'^'988, we have in mean solar hours, oT,= -0-988^^-sin(7iT,-/3) "i And the correction to the maximum is ■ ^cH=E, cos (nT,-l3) Again if T=Ti be the approximate time of minimum, and Tj + cT, the true time, then (53) cTi ^0-988^ sin (7iTi-/5) (54) And the correction to the minimum is m=Hi cos (nTy- ft) In the case of the correction due to (0) + (P))''' is approximately 1 , and for the correction due to Ki, n is approximately l-\ y — <T y — a. §8. Direct Synthesis of the Harmonic Expression for the Tide. The scope of the preceding investigation is the establishment of the nature of the connection between the older treatment of tidal observa- tion and the harmonic method. It appears, however, that if the results of harmonic analysis are to be applied to the numerical computation of a tide-table, then a direct synthesis of the harmonic form may be preferable to a transformation to moon's transit, declinations, and parallaxes. Semidiurnal Tides. "We shall now suppose that M^ is the height of the M^ tide, augmented or diminished by the factor for the particular year of observation, accord- ing to the longitude of the moon's node, and similarly K^ generically for the augmented or diminished height of any of the smaller tides. As ON THE IIARMOXIC ANALYSIS OF TIDAL OBSEKYATIONS. 09 before, let 2/j, 2^' bo the lags of Mo, So ; and 2v, generically, the lag of the K tide. Let 6=l + h-s-y^ + E. Then 6 might be defined as the mean moon's hour-angle, the mean moon coinciding with tlie true, not at Aries, but at the intersection. Let the argument of the K tide be written genericallj' 2\_0 + u~i:']. Then h,=M„eos2(6-fi) + Scos2[8 + s-li + v^-^-!:]+K,cos2[0 + u-K'\ . . . (55) If we write So ^=4 ''o + s, and E cos 2 (ju - f) =M^ + S cos 2[s-Ji- ; „ + ^, ] Hsin 2(^L-f) = S sin 2[..--7i-4o + A']. the first two terms of (55) are united into Hcos2(e-fi>) (56) with fortnightly inequality of time and height defined by tan2(,-^)== S.in2(s-h-i:^ + ,)_^ E= v/ [ ir,2 + ,s2 + 2MS cos 2 (s - 7. - f „ + ^) ] ) The amount of the fortnightly inequality depends to a small extent on the longitude of the moon's node, since (^ 3"tl M^ are both functions of that longitude. For the K tide we have Ka cos 2(d + n — K)=K^ cos 2(u — K + (p) cos 2((i — </.) — Ko sin2(u — K + (p) sin 2(6 — (p). Hence 2H"= K^ cos2(u — K+(j)) ] K .... (58) cf=-^sm2(u-. + ^) ) It is easy to find from the Nautical Almanac (see Moon's Libration) the exact time of mean moon's transit on any day, and then the successive additions of 12''-4206U1 or 12^ 25™ 14sl6 give the successive upper and lower transits. The successive values of 2(s — h) may be easily found by successively adding 12°-6180o6 to the initial value at the time of the first transit of the mean moon, and may be obtained from the table of the fortnightly inequality for each value of 2(.s— 7i). The function ti is slowly varying, e.g., for the K2 tide 2u=2(!i — t,) + 2(i'o — )'"), and the increment of argument for each 12*'-420G01 may be easily computed once for all, and added to the initial value. In the case of the diurnal tides it will probably be most convenient to apply corrections for each independent]}-, following the same lines as those sketched oiit in § 5. The corrections for the over tides M4, S4, &c., and for the terdiurnal 60 KEPOBT— 1885. and quaterdiarnal compound tides, would also require special treatment, which may easily be devised. At ports, where the diurnal tide is neai-ly as large or lai'ger than the semidiurnal, special methods will be necessary. Although the treatment in terms of mean longitudes makes the cor- rections larger than in the other method, yet it appears that the compu- tation of a tide-table may thus be made easier, with less reference to ephemerides, and with amply suflBcient accuracy. Report of the CoTnviittee, consisting of Mr. Robert H. Scott {Secretary), Mr. J. Norman Lockyer, Professor Gr. Gr. Stokes, Professor Balfour Stewart, and Mr. Cf. J. Symons, appointed for the purpose of co-operating with the Meteorological Society of the Mauritius in their propjosed publication of Daily Synoptic Charts of the Indian Ocean from, the year 1861. Dratvn up by Mr. E. H. Scott. The Committee have the honour to forward, for the inspection of tlie members of the Association, a cop}' of the Charts for the month of March 1861, with some specimens for January of the same year, and the com- plete number for February which appeared some years ago. These docu- ments have recently arrived from the Mauritius. As the work has now made decided progress, the Committee have a])plied for and obtained the grant of 50^. placed at their disposal by the General Committee. As soon as the requisite documents are received from Dr. Meldrum, the Committee will submit a formal account of their expenditure with the necessary vouchers. Report of the Committee, consisting of Mr. James N. Shoolbred (Secretary) and Sir William TH0MS0^', appointed for the re- duction and tabidation of Tidal Observations in the English Channel, made ivith the Dover Tide-gauge ; and for connecting them tvith Observations onade on the French coast. Your Committee herewith beg to submit the High Water and the Low Water Observations for the years 1880, 1881, 1^82, and 1888, obtained from the records of the self-registering tide-gauges at the ports of Dover and of Ostend respectively. The observations, in order to facilitate comparisons, are reduced to Greenwich time and to the common datura-plane of 20 feet below the Ordnance datum of Great Britain. As the reduction and tabulation of the present series of tidal observa- tions has proved a longer operation than was anticipated, there has been hardly sufficient time to consider the best form in which those observa- tions should be placed for comparison, nor for the more suitable deductions which may be drawn from such comparison. Your Committee, therefore, request to be reappointed. ON STAXDABDS OF WniTE LIGHT. 61 Report of the Comviittee, consisting of Professor Gr. Forbes (Secre- tary), Captain Abxey, Dr. J. Hopkixsox, Professor W. Gr. Adams, Professor Gr. C. Foster, Lord Rayleigh, Mr. Preece, Professor Schuster, Professor Dewar, Mr. A. Vernon Harcourt, and Pro- fessor Ayrton, appointed for the purpose of reporting on Stand- ards of White Light. Drawn up by Professor Gr. Forbes. The experimental work of tlie Committee during the past year has not been extensive, as they had no funds at their disposal for expei'imental research, and they have been chiefly occupied with reviewing what has been done in the past and laying plans for future operations. Lord Rayleigh has constructed an instrument which he calls a mono- chromatic telescope, by means of which the illuminated screens of a photo- meter may be examined, allowing light only of one definite colour to pass. It was hoped by Lord Rayleigh that experiment might show that, with some suitably chosen colour, this instrument, nsed with any ordinary photometer, would, in comparing lights of different intensities and tem- peratures, give to each a candle-power which would be sufficiently accurate to represent for commercial purposes the intensity of the light. The Secretary has made some experiments at the Society pi Arts, where he was kindly permitted to use the secondary batteries and glow lamps ; but the results so far are not definite enough to justify their publication. Mr. Vernon Harcourt has been engaged on an investigation on the barometrical correction to his pentane standard, and on another con- cerning the possibility of using lamp-shades as a protection from air currents. His researches are communicated independently to the meeting. Captain Abney and General Testing have continued their observations on the intensity of radiations of different wave-lengths from incandescent carbon and platinum filaments at different temperatures, which will go far to assist the Committee in their work. Other isolated experiments have been made by members of the Com- mittee, which will be published in due course. Most of the members have examined the experiments of the Trinity Board at the South Foreland. Existinrj Standards. A consideration of existing standards convinces the Committee that the standard candle, as defined by Act of Parliament, is not in any sense of the word a standard. The French ' bee Carcel ' is also liable to vari- ations ; and with regard to the molten platinum standard of Violle, it seems that the difficulty of applying it is so great as to render its general adoption almost impossible. With regard to the so-called standard candle, the spermaceti em- ployed is not a definite chemical substance, and is mixed with other materials, and the constitution of the wick is not suflSciently well defined. Hence it is notorious that interested parties may prepare candles con- forming to the definitions of the Act which shall favour either the pro- ducer or consumer to a serious extent. In view of these defects of the standard candle, it is a matter of great importance that a standard of light should be chosen which is more certain in its indications. The Committee have looked into the merits of different proposed standards, and the majority feel satisfied that, for all the present com- G2 REroRT— 1885. mercial requirements, the pentane standard of Mr. Yernoii Harcourt — since it lias no wick and consumes a material of definite chemical com- position — when properly defined, is an accurate and convenient standard, and gives more accurately than the so-called standard candle an illumi- nation equal to that which was intended when the Act was framed. Yet the Committee, while desiring to impress the Board of Trade and the public with these views, do not feel inclined at present to recommend the adoption of any standai'd for universal adoption until, further in- formation on radiation having been obtained from experiment, they may learn whether or not it may be possible to propose an absolute standard, founded, like electrical and other stpndavds, on fundamental units of measurement — a standard which, for these reasons, would be acceptable to all civilised nations. They are, howevei', inclined to look upon the pentane lamp as an accurate means of obtaining an illumination to replace the so-called standard candle. Froposed Experimental Hesearcltes. Radiation is measured as a rate of doing work, and consequently radiation might be measured in watts. The illumination (or luminous effect of radiation) depends partly upon the eye, and is a certain function of the total radiation. This function depends upon the wave-length of the radiation, or on the different wave-lengths of whicli the radiation, if it be compound, is composed. This function of the radiation perceived by the eye is partly subjective, and varies with radiations of different wave-lengths and with different eyes. Thus the illumination cannot, like the radiation, be expressed directly in ab.^olute measurement. But the connection between the illumination and the radiation can be determined from a large number of experiments with a large number of eyes, so as to get the value of the function for the normal liuman eye. This function, however, is constant only for one source of light, or, it may be, for sources of light of the same temperature. It appears, then, that, in the first instance at least, a standard should be defined as being made of a definite material at a s-pecial temperature. The energy required to produce a certain radiation in the case of a thin filament of carbon or platinum-iridium heated by the passage of an electric current can be easily measured by the ordinary electric methods, and the radiation may be measured by a thermopile or a bolometer, which itself can be standardised by measuring the radiation from a definite surface at 100° C, compared with the same at 0° C. The electric method measures the absorption of energy ; the thermopile measures the total radiation. These two are identical if no energy is wasted in convection within the glass bulb of the lamp, by reflection and absorption of the glass, and by conduction ffom the terminals of the filament. Captain Abney and General Festing have come to the conclusion that there is no sensible loss from these causes. The Committee propose to investigate this further. This constitutes a first research. No research is necessary to prove that vvith a constant temperatui'e of a given filament the luminosity is proportional to the radiation, because each of these depends only upon the amount of surface of the radiating filament. It will be necessary, however, to examine whether with different filaments it be possible to maintain them at such temperatures as shall make the illumination of each proportional to the radiation. This will be the case if spectrum curve^', giving the intensity of radiation in ON STANDAKDS OF WHITE LIGHT. 63 terms of tl\c wa%-e-lengtli when made oiTfc for tbe different sources of light, are of the same form. Thus a second research must be undertaken to discover whether the infinite number of spectrum radiation curves, which can be obtained from a carbon filament by varying the current, are identical in form wiion the filament is changed, but the material remains so far as possible of constant composition. It will be an object for a later research to determine whether, when the radiation spectrum curve of any source of light has been mapped, a similar curve can be found among the infinite number of curves which can be obtained from a single filament. The next stc]) proposed is to e.\amine a large number of carbon or of platinum-iridinm filaments, and to find whether the radiation spectrum curve of different specimens of the same material is identical when the resistance is changed in all to x times the resistance at 0° C. If this law be true, a measurement of the resistance of the filament would be a convenient statement of the nature of the radiation curve. If, then, a number of filaments were thus tested to give the same radiation spectrum curve, their luminosities would in all cases be proportional to their radiations, or (if there be no loss in convection, conduction, absorption, and reflection) proportional to the electrical energies consumed. Thus it might be hoped to establish a standard of white light, and to dctlneit somewhat in the following manner: — ^4 zinit of light is ohtained from a straigJit carbon fila'inent, in the direction at right angles to the middle of the filament, when the resistance of the filament is one-half of its resistance at 0° C, and when it consumeslO^ C.G.S. units of electrical energyper second. Since Mr. Swan has taught ns how to make carbon filaments of constant section by passing the material of which they are composed throuo-h a die, it is conceivable that another absolute standard should be possible — viz., a carbon filament of circular section, with a surface, say, TiTij ^l- centimetre, and consuming, say, 10^ C.G.S. units of energy per second. Whether such standards are possible or not depends npon the experi- ments of the Committee. The probability of success is suflBcient to render these experiments desirable. Proposed Later Experimental Researches. Should these hopes be realised, and an absolute standard of white light thus obtained of a character which would commend it to the civilised world, it would then become an object of the Committee to find the ratio of luminosity when the radiation spectrum curve of the standard filament is varied by varying the current, and consequently the resistance of the filament. Thus, by a large number of subjective experiments on human eyes, a multiplier would be found to express the illumination from the standard lamp, with each degree of resistance of the filament. A reseai'ch, previou.sly hinted at, would then be undertaken — viz., to find whether the radiation spectrum curves of all sources of illumination agree with one or other of the curves of the standard filament. It is not improbable that this should be the case except for the high temperature of the electric arc. Should this be found to be true, then photometry would be very accurate, and the process would be as follows: — Adjust the standard fila- ment until its radiation spectrum curve is similar to that of the lijht to he 64 REPORT — 1885. compared. (This would probably be best done by obsei'ving tlie wave- length, of the maximum radiation, or by observing equal altitudes on either side of the maximum, the instruments used being a spectroscope and a line thermopile or a bolometer.) The total radiation of each is then measured at equal distances by the thermopile. The resistance of the filament is measured, and its intensity in terms of the unit of white light obtained therefi-om by the previous research. The luminosity of the compared source of light is then obtained directly. The Committee desire to be reappointed, and to enable them to carry out the researches indicated they ask for a grant of 30^. Second Report of the Committee, consisting of Professor Balfour Stewart (Secretary), JNIr. J. Knox Laughton, Mr. Gr. J. Symons, ]Mr. R. H. Scott, and Mr. Johnstone Stoney, appointed for the purpose of co-opjerating luith Mr. E. J. Lowe in his pjroject of establishing a Meteorological Observatory near Chepstow on a permanent and scientific basis. Since theh- reappointment in 1884 this Committee have met twice, and have placed themselves in correspondence with Mr. Lowe. In this correspondence the Committee have expressed their opinion that the establishment of a permanently endowed meteorological observa- tory ou a good site, such as that of Shire Newton, is a matter of undeniable scientific importance. The attitude whicli the Committee have taken will be rendered appa- rent by the following letter written by their Secretary to Mr. Lowe : — ' The Committee request me to point out to yoa that the main feature of your proposal, which interests the British Association and the scientific public generally, is the prospect which it holds out of the establishment o? a permanent institution by means of which meteorological constants could be determined, and any secular change which may take place therein in the course of a long period of years be ascertained. It will be for you and the local authorities to decide what amount of work of local interest should be contemplated, and on this will the scale of the observa- tory mainly depend. The Committee are therefore unable to say what amount of capital would be required. They would point out four con- ditions which they hold to be indispensable : — '1. The area of ground appropriated should be sufficient to ensure freedom from the effect of subsequent building in the neighbourhood. ' 2. A sufficient endowment fund of at least 150L annually should be created. ' 3. The control should be in the hands of a body which is in itself permanent as far as can be foreseen. ' 4. The land for the site shall be handed over absolutely to the above- mentioned governing body.' This communication from the Committee is now under the considera- tion of Mr. Lowe and his friends, but until the precise amount of the local meteorological requirements is ascertained and further progress is made in the scheme the Committee consider that they would not be justi- fied in any more prominent action than that which they have already taken. They would request their reappointment, and that the unexpended sum of 2hl. be again placed at their disposal. ON COMPARING AND EEDUCING MAGNETIC OBSERYATIONS. 65 Report of the Committee, consisting of Professor Balfour Stewart {Secretary), Sir W. Thomson, Sir J. H. Lefroy, Sir Frederick Evans, Professor Gr. H. Darwin, Professor Gr. Chrystal, Professor S. J. Perry, Mr. C. H. Carpmael, and Professor Schuster, appointed for the purpose of considering the best means of Com/paring and Reducing Magnetic Observations. Brawn up by Professor Balfour Stewart. In presenting their report to the Britisli Association the Committee would begin by referring to the appendix, in which are embodied sug- gestions of great value which they have received from men of science at home and abroad. The Committee desire to express their thanks to the authors of these contributions. While a final discussion of these communications cannot be attempted in this first report, it is nevertheless evident that magneticians are not agreed as to the best method of determining absolutely the solar-diurnal variations of the three magnetic elements — that is to say, the diurnal variation resulting after the elimination of all disturbed obsei'vations. The point in dispute is the method of distinguishing and separating the disturbed from the undisturbed observations. On the whole, the feeling is against the method of Sabine, on account of the arbitrary nature of his separating value. An alternative method has been proposed by Dr. Wild, Director of the Central Russian Observatory (Appendix, No. VII.). This method seems to be in some degree analogous to that pursued at Greenwich (Appendix, No. IX.). Dr. Wild selects those curves which appear to the eye to be free from the short-period irregularities characteristic of disturbances, and considers the results obtained from their measurement to embody a trustworthy representation of the solar- diiirnal variation for the time and place in question. He finds a remarkable uniformity and simplicity of type in the variation as given by the difi"erent selected curves. While the Committee recognise in this a method which may ultimately meet with general acceptance, they think there are various points con- nected with it which require investigation. In the first place, it would be desirable to prove, by means of an exhaustive discussion of some one element — as, for instance, the declina- tion — to what extent curves selected by the eye do, as a matter of fact, present this uniformity and simplicity of type. There are abundant materials available for this purpose at the Kew Observatory, and it is hoped that through the kindness of the Kew Committee this point may eventually be settled. Again, it would be desirable to ascertain whether the apparently normal days at one station coincide with those at another ; and, if so, whether there is a definite or nearly definite relation in type and range between the corresponding smooth curves of two widely separated stations of not very dissimilar latitude. This point will form one of the subjects of a discussion undertaken by Sir J. Henry Lefroy, who proposes to compare the curves of Toronto and those of Greenwich together for the years 1849-53. 1885. F 66 REPORT — 1885. The Committee are of opinion that these are steps \vhich might at once be taken, so as to push on this part of the subject. The Committee -would call attention to the completeness of the mag- netical information which is given by the present method of publication adopted by the Astronomer Royal. He now gives, in addition to the mean values of the magnetic elements for each day and the mean diurnal curves for each month, the amplitade of the diurnal curve for each day, and particulars of all disturbances, small as well as large. (See Appendix, No. IX.) Until a method is generally accepted for determining the normal solar- diurnal valuation, it seems prematui-e to raise any discussion on the best ■way of estimating disturbances, since these cannot well be measured except from the basis of such a normal. The Committee would, however, allude to various investigations, chiefly connected with disturbance, which are being undertaken by some of its members. The thought seems generally to have occurred that dis- turbances may denote the method by which the earth rights itself with respect to the magnetic forces acting upon it (see Appendix, No. II., para- graphs 11 and 12), and this idea underlies the various researches about to be named.' The first of these is that already mentioned as having been taken up by Sir J. H. Lefroy, with the concurrence of the Astronomer Royal — namely, a comparison oi magnetic movements photographically recorded at Toronto and Greenwich in the years 1849-53. Stations so far asunder (3,100 miles), and on different continents, appear calculated to throw light on many questions which are not much advanced by compaiison of stations in geographical proximity. The following are i^ri ma facie conclusions which may require modifica- tion when the work has been gone through, but which already seem to have a bearing on the physical explanation of the phenomena : — a. A similar state of magnetic weather, so to speak, prevails generally at both stations, so that where numerous or extensive deviations from normal regularity occur at the one, there is generally something corre- sponding at the other. h. The correspondence very seldom amounts to similarity of movement or identity of time. c. The changes of declination at Toronto are more rapid than at Greenwich. This is especially observable about the time of the morning easterly extreme. Bold sweeping curves with a long time measure are much less common at Toronto than at Greenwich, and can seldom be identified. d. On the other hand, shocks of small angular amount breaking a uniform line are often capable of identification, and are simultaneous, or nearly so, at both stations. e. Although the declination was westerly at both stations, the move- ments of disturbance are very frequently, probably usually, in opposite directions at any given time — easterly at Greenwich, or decreasing the absolute declination, when they are westerly, or increasing it, at Toronto. /. The same days would generally be selected to form normal curves at both stations. > A similar idea seems to have occurred to Dr. Wild (see foot-note to his communi- cation, Appendix, No. VII.). ON COMPARING AND EEDUCING MAGNETIC OBSERVATIONS. 67 g. Sliglit auroral displays in Canada generally produce a mai'ked effect at Toronto, but none at Greenwich. h. It is not easy to answer the question whether a state of disturbance succeeding one of calm begins or ends at the same time at both stations, neither beginning or ending being, in general, sufficiently definitely marked. i. It appears impossible to assign a value based on angular movement alone which will be a valid test, whether such movement is due to dis- turbing causes or not. j. Angular movements at Toronto appear to be larger than at Green- wich, the magnets being (in 1849-50) similar — namely, 2 feet in length. The second research is by the Rev. S. J. Perry and Professor Stewart, who, with the sanction of the Kew Committee, are engaged in a com- parison of the simultaneous disturbances of the declination at Stonyhurst and at Kew. Calhng the first S, and the second K, they have obtained the following preliminary results, which may, however, ultimately require some modification : — (1) S is always greater than K, or the ratio ^ is always greater than unity. • (2) This ratio appears to depend in some way on the duration of the disturbance. (3) But not, as far as can be seen at present, upon its magnitude. A third research is by Professor Stewart and Mr. W. Lant Carpenter, who are making a preliminary trial of four years of Kew declination dis- turbances (separated by Sabine's method), in order to ascertain whether the aggregate daily disturbance depends upon the relative position of the sun and moon, and also whether it is affected by meteorological storms. The following provisional result has been obtained from the years 1870-73 in which the lunation is divided into 8 parts, (0) denoting new, and (4) full moon. Mean Daily Aggregate of Disturbance of Declination at Kew} (Unit xo^^'b of an inch, measured on the curve.) (0) (1) (2) (3) (4) (5) (6) (7) 111 114 104 95 83 94 107 101 The Committee desire to draw the attention of magneticians to the urgent need of obtaining more accurate knowledge than we possess at present of the daily variation of the vertical force. No attempt to fix the cause of the daily variation can be made until the daily variation of each component of the magnetic force is known. In conclusion, the Committee desire their reappointment, with the addition to their number of Captain Creak and of Mr. G. M. Whipple, Director of the Kew Observatory, and they would request that the sum of 50Z. should be placed at their disposal, to be spent as they may think best on the researches mentioned in this report. ' The late Professor J. Clerk Maxwell was, it is believed, the first to suggest that the lunar-diurnal variation of the earth's magnetism maybe caused by distortion, and Dr. Schuster has suggested that, if there is found to be a relation between magnetic disturbances and atmos]pheric storms, it may be of the same nature. f2 68 REPORT — 1885. APPENDIX. Suggestions for the Committee on Magneticcd Reductions. I. By Professor Balfoue Stewakt, F.R.S. 1. The following suggestions are founded on the methods proposed by several magneticians, including Sabine, Broun, Lefroy, Capello, and Buys Ballot. To Senhor Capello I am especially indebted for the trouble he has taken in explaining his views, with which these suggestions are almost identical. 2. The measurements derived from self-recording magnetographs may be used for two purposes, the first being to ascertain the solar diurnal variation, by which name we designate that variation which is exhibited by comparatively undisturbed observations. The second of these pur- poses is to ascertain the laivs ivliich regulate Jisturhances. Now disturbances may act in two ways. First, they may exhibit a diurnal variation different from that of the undisturbed observations, which we may call the dis- hcrhance diurnal variation ; and, secondly, they may exalt or depress the ^ day's value of the particular element in question. As a matter of fact I believe they act in both these ways. It appearsi to me that it is of very great importance that these two effects of dis-l turbance should be exhibited and studied togertier, and yet not impro- perly mixed up with one another. 3. Let me explain my meaning with reference to the method of Sabine,! ■which I believe to be, in many respects, an excellent one. Sabine did very great deal in finding out and exhibiting the diurnal variations of the' disturbed and undisturbed observations, but he did not greatly study, along with these, the effect of disturbances in altering the daily mean values of an element, so that it was reserved for Broun to discover that there were changes in the daily values of the horizontal force which were practically simultaneous at the various stations of the globe. Let us fii-st of all consider the hourly values of declination, as this element presents fewest difficulties. Declination, 4. Here, I imagine, the first thing is to determine the solar diurnal variation, or that presented by the comparatively undisturbed observations, and for this purpose I fail to see a better plan than that proposed by Sabine. This method may be described as follows : 5. Suppose that we have hourly observations at a station, then, first of all, we should arrange these into monthly groups, each hour by itself. We should then reject, as disturbed observations, all those which differ by more than a certain amount from their respective normals of the same month and hour, the normals being the hourly means in each month after the exclusion of all the disturbed observations. For the purpose of ascertaining the true solar diurnal variation, it seems probable that a considerable choice might be allowed in selecting the separating value implied in the above process, one value serving, for tliis pii^rpose, probably as well as another a little above or below it. 6. Perhaps under ordinary circumstances a value which will exclude as disturbed about one-twentieth of the whole body of observations will be found convenient. 7. Let us now imagine that we have determined by this process ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 69 the undisturbed normpJs for eacli hour, for each month. I agree -with Sir J. H. Lefroy in thinking that the best plan of investigating disturb, ances is, in the first place, to obtain the various departures of individual observations from their respective normals for that month and hour. It would be desirable to embody these departures in a fresh table, in which (except for those who are colour-blind) the negative departures might be given in red ink and the positive in black. 8. In this table, at the right of the twenty-four departures for the various hours of the day, I should represent the mean departure for that whole day either in red or black. It would thus be seen, at a glance, whether the average of the whole day was affected by disturbance, in what direction, and to what extent. 9. It is here assumed that, during the month in question, no alteration of scale value or other instrumental change has taken place. Never- theless at stations which have a considerable secular variation of decli- nation, and for which this is known, it might be desirable to introduce, say to the extreme right, a column embracing a small residual correction, applicable to each day's departures, on account of secular change. 10. I imagine that a monthly table, constructed after the method which I have described, will afford a full and satisfactory basis for the discussion of disturbances. 11. It is probable that the smaller departures will follow the law of the ordinary solar diarnal variation, and, in that case, there should be as many Ijlach as red sums in these minor departures, or, in other words, the algeiaraic sum of these should be zero, while the sum taken without respect to sign or colour should represent the amount of oscillation or disturbance obeying the ordinary law, this being a point which it is of interest to determine. No doubt the larger disturbances will obey some other law, and it will be necessary to separate them into two categories, those increasing and those diminishing the declination. Here I should follow Dr. Buys Ballot's advice, and allow the observations themselves to determine where the one law ends and the other begins. It is just possible that sometimes the day's mean may be decidedly different fi'om what it ought to be, and yet the diurnal variation for that day be as nearly as possible the same as for undisturbed observations. A table, such as that now described, will show, at a glance, whether such a state of things ever takes place. Horizontal and Vertical Force. 12. The horizontal and vertical force magnetographs are different from the declination magnetograph, inasmuch as their indications are affected by change of temperature, by loss of magnetism, and possibly, in the case of the vertical force instrument, by other circumstances not well understood. 13. It will be noticed that, in treating the declination results by Sabine's method, we perform oar operation upon the individual declina- tion values. Now it might be said, why not (your object being to find the solar diurnal variation) take the dej^arture of the individual hours of a day from the mean of that day, and treat each month's departures by Sabine's method ? 14. The reply would be that the mean of a day is more likely to be affected by disturbance than the monthly mean of an hour. For disturb- ances, when they come, generally affect several consecutive hours, thus 70 REPORT — 1885. altering the daily mean, but, on the other hand, they are less likely to affect the same hour during consecutive days. Were we able to obtain daily means of declination, unaffected by disturbance, it would be better to adopt this method of treatment, because it would obviate the intro- duction of any residual correction due to the progress of secular change or annual or semi-annual variation. Now in the force magnetographs the case is different. Here there is a certainty that some — perhaps even a considerable — change will be produced in the values belonging to a given hour in the course of a month from instrumental changes alone, so that treating the observations after the manner pursued with the declination might lead to erroneous results. 15. On the other hand, if there were no disturbance, the difference of the various hourly observations of a day, from the mean of that day, would give us a good indication of the solar diurnal vai-iation, provided the diurnal range of temperature was inconsiderable, as is generally the case for self-recording instruments. 16. These remarks render it manifest that some method of obtaining- probable values of the undisturbed daily means is, in the case of the force instruments, of vital importance, and Senhor Capello has adopted a method of this kind in his treatment of his force observations. I would venture to remark that the most unexceptionable basis upon which to determine the undisturbed daily means of horizontal and vertical force would seem to be given by the information already assumed to be obtained from the declination magnetograph for the same month. 17. Here, as a result of the application of Sabine's method, we have rejected a certain number of hourly observations as disturbed. Now let us reject, as a preliminary step to something more complete, precisely the same hourly observations of the horizontal and vertical force as being, in all probability, disturbed, and make use of the remainder, or of that part of the remainder which represents whole, or nearly whole, days free from disturbance, to aid us in determining, by a curve, the most probable values of the undisturbed daily means. I here assume that there is no sudden jump in the month's readings from change made on the instrument or any other cause ; if there be such, the portions before and after the jump will have different values, and must be treated by appropriate methods which need not here be discussed. Suffice it to say that, by rejecting from the month's observations those hours which were separated as dis- turbed in the declination, and treating the remainder in the manner suggested, we obtain, aided, perhaps, by a slight equalisation, numbers representing very nearly the undisturbed daily values of the records given by the insti'uments. 18. Having obtained these, our next operation is to obtain the hourly differences from each day's undisturbed mean. These differences, so obtained, we i^ropose to treat in the same manner in which we treated actual declination observations. It is, therefore, to these differences that Sabine's process should be applied, so that ultimately, when we have applied it, we shall obtain those departures of each hour from the daily mean which characterise undisturbed observations — in other words, we obtain the solar diurnal variation. 19. Having obtained this, we have at once the means of obtaining a table similar, in all respects, to that which we have recommended for the declination. For instance, if the departtire of a given hour of a given day from the undisturbed mean of that day were + 9 whereas, according ON COMPAEING AND KEDUCINa MAGNETIC OBSERVATIONS. 71 to the solar diurnal variation for undisturbed observations, it should have been +3, the number +6 would be inserted in the table, and so on. 20. It will be seen at once that we shall be able to ascertain by the method now described, if disturbance (as Broun supposed) alters the daily average values of the horizontal force. For in the horizontal force instrument any comparatively short period change of average daily value is hardly likely to be caused by instrumental alteration, but is most pro- bably due to magnetic causes, more especially if the same change take? place simultaneously at various stations. There are, however, moi-e serious difficulties connected with the vertical force instrument, but into these I cannot now enter. II. By Sir J. Hexet Lefeot, K.C.M.G., F.R.S. 1. The statement of the question appears to assume that the first, or chief, object of continuous automatic registers of magnetic changes is to extend the large number we already possess of mean determinations of solar-diurnal variations, and to add fresh numerical or quantitative values of the deviations from these means, produced by the causes we class as irregular. 2 . This appears to me to be persevering in a path we have been travel- ling for forty years Avithout reaching, or even seeing the way, to any physical explanation of the phenomena. 3. There are about seventy-five points on the globe at which the diurnal variation, including disturbances, has been determined by eye- observations, hourly or bi-hourly, with more or less completeness and precision. The irregular, or non-solar-diurnal, effects have as yet been eliminated for a few only (ten or twelve) of these points, but this number has proved sufficient to bring out pretty clearly certain general laws to which no key has yet been found. 4. Unless it can be shown, that a multiplication of numerical data promises to bring us to a conclusion, I am inclined to think that the laborious compilation of more data of the same kind by measurements from photographic registers, which are less precise than the old eye- observations, is rather a misdirection of energy, unless indeed at stations widely remote from any others, and where new facts may be expected (see, for example, the very anomalous diurnal curve at Reikiavik, Iceland, 'Athabasca volume,' p. 297). The recent circumpolar stations would have come into this category if they had used self-recording instruments. 5. Airy and Sabine have both taken ± 3'"3 of declination as the measure of a disturbed observation at Greenwich and Kew respectively.' If it is true, as remarked by Professor Balfour Stewart (par. 5), that the precise measure is of no great consequence, is it worth while to spend much time over making out a new value independently for any part of Great Britain ? 6. The arbitrary nature of Sabine's mode of treatment of observations is to me a strong objection to the continuance of it. For example, he threw out as disturbed all the observations at Point Barrow which deviated 22'-87 from the normal,^ and at Fort Carlton ^ all which deviated 6'-0. But I think I have sufficiently shown that in high latitudes in America the mean value of disturbance is about three times ' Phil. Trans. 1860-1863. - Phil. Trans. 1S57. ^ St. Helena, vol. ii. 72 EEPOET 1880, as great in the early morning hours as it is in the afternoon. Conse- quently we must either disregard a great many observations by day, which are really disturbed, or include a great many by night, which are not, unless we say that instability is the same thing as disturbance. 7. What, then, is to be done with the photographic registers ? How can they be compared unless by ordinates, measured at points agreed upon, such as the Gottingen hours ? I reply (1) that I think that each observer should minutely scan his own records, and note the time, direction, and amount of movements. (2) That the efiPorts of magneticians should be addressed to the cheap pulolication and prompt interchange of the registers of each week, reproduced and reduced by photography to a uniform scale, say 15mm. to 1 hour, with a view to the discovery of periodically recurring movements of whatever nature ; of movements apparently local, or not generally traceable ; and of movements which were general, in one or more elements, over a large part of the earth's surface. It hardly meets this suggestion to say that we have hundreds of projections of disturbances already, and that nothing has come of it. It is true ; but these projections are scattered through many volumes, are upon all sorts of scales, and are rarely comparative. 8. The student having by his eye- comparison grasped the general features of the movements constituting disturbance at some particular epoch, or presenting an exceptional character, the need of measurements would arise, and if a reference to the mean of the day or the mean of n days or of the calendar month is necessary, such mean can be ascertained. I am not sure that it often will be, and I doubt whether our adherence to the calendar month is rational. Why should movements on May 31 be referred to the mean for May rather than the mean for June ? The more accurate, though more laborious, plan would be to refer them to the mean for May 31 ± 10 days. 9. The end of the needle which points to the equatorial region has in every locality a mean position in relation to the meridian from which it is continually deviating, and to which it always returns. It appears to me open to question whether the relation of the direction of the move- ment to the absolute declination, as increasing it or diminishing it, has much to do with the question. At least it seems to assume that the normal position is due to the same physical causes as produce the devia- tions, and therefore I think that the deviations, whether of the polar or equatorial end, should be simply noted as east or west without regard to sign. In the southern hemisphere it is the equatorial end that we observe. Eegions where the north end is actually directed to the south, as at Port Kennedy and the Alert's winter quarters (1875-6), will require negative signs. 10. It seems probable (1) that the mean position of the needle above referred to is always perpendicular to the direction of electric currents in the crust of the earth, or the atmosphere, or both, originating in a thermo- electric action of the sun on the meridian, and propagated north and south from the ecliptic ; (2) that the position of the meridian of the place, in reference to the sun, determines the direction of the mean deviation of the needle from its normal position or the mean solar-diurnal movement, and that the amount is determined by a balance of forces still to be clearly defined. The amount is known at a sufficient number of stations to test any law laid down. ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 1 3 11. Ifc appears that so long as the sun is above the horizon of the place, there is comparatively little disturbance. In other words, the hours most habitually disturbed are before sunrise and after sunset. It is true that disturbances, once originated, display themselves simultaneously at dis- tant localities, irrespective of the hours of the day ; but the above seems to give probability to a conjecture that they originate in that hemisphere from which the sun is absent, and on those meridians which are at the time in the condition of greatest mean disturbance. 12. Of known physical causes, the influence of sudden internal per- turbations analogous to those which become perceptible to our senses, as earthquakes and the like, seems to me the most nearly to meet the observed facts. They cannot be due to any atmospheric cause. Nor is it very probable that anything extra-terrestrial, such as solar perturbations, can operate with such vigour and suddenness upon our electric circula- tion. That there is a sympathy or correspondence between seismic dis- turbance and magnetic disturbance has been often shown, but I am not aware that it has ever been followed up in a comprehensive way. That this view implies some relation between the internal perturba- tions referred to, and the position of the part of the globe in which they originate in respect to the sun, as being in the hemisphere turned away from him, appears to follow, but I do not see any absurdity in such a supposition. 13. Since continuous automatic registration affords a means of tracing the coi'respondence of either short-time or long-time movements with other observed phenomena, seismic movements, solar outbursts, auroral discharges, and atmospheric changes, for example such as no multiplication of eye-observations can do, this appears to me the first use to put it to. Forty years of eye-observation have added enormously to our store of facts, but brought us little if anything nearer a theory. Is it not time to try some other line of investigation ? 14. With respect to the behaviour of the horizontal component during disturbances, depending as it does upon two variables, the dip and total force, it is rather unsatisfactory, but we have good and extensive data, and whatever principle of measurement or solution is applied to, the declination, must, I apprehend, be extended to this element. 15. With respect to the vertical component I doubt whether the available data are as yet comparable in precision with those of the other two elements. I saw, however, some admirable curves at Toronto, pro- duced by Professor Carpmael's new instrument (I feel doubtful now whether they were curves of A Y or A0), which had all the character and freedom of those of the horizontal force, and when these have been worked np and discussed we shall know a good deal more about the influence of disturbances in increasing or diminishing the dip and total force. III. By Professor Schuster, F.R.S. I should like to submit to the Committee a few points to which their attention, in my opinion, might with advantage be directed. It is now nearly fifty years since Gauss applied the method of expan- sion in spherical harmonics to the elements of terrestrial magnetism. He considered his results only as preliminary, on account of the incomplete- ness of the data on which he had to work. 74 EEPORT — 1885. We possess now so much more information on the mean value of the terrestrial elements at different places, that, it seems to me, a repetition of the calculations of Gauss would lead to valuable results. Such a cal- culation would not only be of theoretical importance. For we might in this way detect many points of interest, as, for instance, where if anywhere masses of iron are present near the surface of the earth in sufficient quantity to affect the magnetic elements. At such places we should ex- pect the harmonic analysis to give correct results only if extended to a large number of terms, so that if we confine ourselves, like Gauss, to four or five terms only, and find considerable differences between the calculated and observed values at some part of the earth's surface, we should have our attention specially directed to that part. It is only by a reduction such as that of Gauss that we shall be able to find out where we require further observations, and where a multiplica- tion of observations is unnecessary. It would be very desirable if we could extend the analysis of spherical harmonics to the daily variation of the elements and to magnetic dis- turbances generally. But it seems to me that if, as is likely, these changes are due to electric currents either above or below the earth's surface but near it, the analysis would have to be carried to a large number of terms before it would yield satisfactory results. But this, of course, is a matter which the actual calculation only can settle, and we ought therefore, at any rate, to make the attempt to apply the method of Gauss to the daily variation. With our present knowledge of that variation at different places of the earth's surfaces, there ought to be no difficulty in finding out whether five or six terms are sufficient to represeut it, taking ac- count, of course, also of those terms which have their origin outside the earth. Some observations of Sabine made near the magnetic pole " seem to point to the fact that part of the diurnal variation is due to a vertical component of an electric current crossing the earth's surface. Whether such a vertical component exists can be determined without difficulty, for we can actually measure it by taking the line integral of magnetic force at a given time over a closed curve on the earth's surface. I should like, therefore, to propose to the Committee to find out, in the first place, what determinations of the magnetic elements ought to be taken account of in the reductions. In countries where we possess a great number of accurate data, it would seem only an increase of labour to take account of all of them. On the other hand, where we possess few measurements we should in all probability have to use even approximate determinations. It is a point for the Committee to decide whether we ought to take the places which are to be included in the calculation spread as evenly as possible over the earth's surface, or whether a preponderance should be given to places near the magnetic poles or at other places of special importance. Also whether the more accui'ate observations ought to be weighed. Should the Committee approve of these reduction.=5, it would be well to ask at the next meeting of the Association for a sufficient grant to engage the assistance of one or two computers. I should like in conclusion to submit a few observations respecting the remarks made by Professor Balfour Stewart and Sir Henry Lefroy. The function of the Committee seems to me to be a double one. In the ' See Encyclopedia Britannica — Terrestrial Magnetism (art. Meteorology). ON COMPAKING AND EEDUCING MAGNETIC OBSERVATIONS. 75 first place, they are to discuss the best methods of reducing magnetic ob- servations ; but, before these methods can be put into execution, we must secure that the observations taken at different places are sufficiently homogeneous to admit of a common treatment. As we have to deal not with the individual observations, but with numbers which have already been reduced at the different observatories, it is clearly of importance that these preliminary reductions should be done everywhere in the same manner. Professor Stewart's suggestions refer exclusively to this point, while Sir Henry Lefroy rather discusses the question as to how the measure- ments already in existence can be made to yield information of physical value, and as they are treating of different matters, there does not seem to me to be necessarily any real difference of opinion between them. While agreeing entirely with a great many of the remarks made by Sir Henry Lefroy, I believe that some common method of reduction like that proposed by Professor Stewart is necessary before we can gain any know- ledge of magnetical disturbances. With regard to the proposals them- selves, the principal question will always be, whether the different heads of observatoi'ies can be made to agree on a uniform plan. The exact nature of the method of reduction is a matter which has to be settled chiefly by those who have practical experience in magnetic observatories. The method of rejecting disturbed observations, commented upon by Sir Henry Lefroy, is, no doubt, open to objection. If it was simply our object to gain information on the mean value of magnetic elements, no observation however much disturbed ought to be rejected ; but as soon as we suspect that the mean value is not the normal value — that is to say, that disturbances act more frequently in one direction than in another — we are necessarily driven to adopt some method of rejecting disturbed observations. The objections raised by Sir Henry Lefroy against the par- ticular method employed by Sabine seem to me to be, however, very serious, but I can see no difficulty in amending that method so as to render it free of the difficulty. IV. Letter from Professor 0. H. Darwin, F.R.S. Cambridge : June 10, 1885. A 'priori I should not have thought of distinguishing between mean and normal values, but I suppose that it is desirable to do so. It is obvious that if all the observations for a month are analysed, we get the mean harmonic constituents. Then if we recompute the values with these constituents (which may be done with a tide predicter), and sub- tract the hourly values from the observations originally analysed, we get a series of residuals. Supposing from those residuals we arbitrarily cut out a certain number which are above some arbitrarily chosen magnitude, and submit the rest to harmonic analyses, and supposing these presen1> us with a new series of constituents with pretty constant phases and amplitudes, then it would seem to me that we should be justified in the hypothesis that normal and mean are not the same thing. I must suppose that some process more or less equivalent to this has been carried out. I do not observe that any proposal is made to submit the monthly constants derived from harmonic analysis to a further analysis, and thus to derive the annual, semiannual, and terannual inequalities of the con- 76 EEPORT — 1885. stituents. My meaning is tliat we ought to express the result in sets of terms of this form. Aq + A, cos e + A„ cos 2 + . . .1 + ai sin B + a, sin 2^+ . . . .]^^^ '? Bo + B, cos + Bo cos 2 e 4- . . . ■) . + &i sin a + io 'sin 2 + . . . . / ^^^ ?* I had some time back a letter from Chambers at Bombay in which he says that he considers he has detected a lunar inequality. Now, unless this is certainly incorrect, is it not desirable to submit the quantities to analysis according to lunar time ? I take it that your proposal as to spherical harmonic representation is to put the Aq, Aj, A2, aj, ag, &c., as constants multiplied by spherical liarmonic functions of the latitude and longitude of the place of observation, Gauss had, as I fancy, only considered the mean values in this way, and you are proposing to treat the diurnal inequality in a similar manner. If much harmonic analysis is to be done, some form nearly like that used for tidal reductions would seem to be useful. The chief complication of those forms consists in the fact that the tide-heights are taken at exact solar hours, whereas we want measure- ments taken also at mean lunar and a number of other kind of hours. All this is avoided in your case, unless indeed you carry out an analysis for the alleged lunar influence. Yours sincerely, G. H. Darwin. V. 'Motes on the above Suggestions. By Professor Balfour Stewaet. The suggestions of the Committee are invited upon the following points : 1. Do they agree with the suggestion of Dr. Schuster, that it is of importance to ascertain the solar-diurnal variation of the three magnetic elements at various stations of the earth's surface, with the view of treat- ing these after the method of Gauss ? 2. Assuming that observations made at stations near the magnetic pole need special treatment, do the Committee think with Sir Henry Lefroy that even in ordinary localities the method of Sabine is objection- able for obtaining a correct value of the solar-diurnal variation ? As a good many declination observations have been treated by this method it is of importance to set the question at rest, and the suggestions of .the Committee are invited as to the best means of doing this. 3. What do the Committee think of the herein-recorded method of obtaining the solar-diurnal variations in the case of the hoi'izontal and vertical force instruments ? I may state that a point of immediate scientific importance arises regarding the V. F. solar-diurnal variation, inasmuch as the observers at Lisbon and Bombay suspect that this, unlike the diurnal variations of the other two elements, does not vary with the state of the sun's surface. It would be very desirable to obtain con- clusive evidence of this from other stations. ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 77 VI. Bemarlcs on Magnetic Reductions. By Senhor Capello. The method of the separation of the disturbances of the readings of the bifilar and the vertical force, of which I have sent a resume, and the examples of the calculation of the last year, seems practical enough to me, although it will give some trouble. It has, however, retained the prin- cipal fault, the arbitrary nature of the quantity which constitutes the disturbance. To practise this method upon the hourly observations of the vertical force is not, I think, more difficult than upon the bifilar. With respect to the vertical-force instrument of this observatory, I do not find it very inferior to the bifilar, except for some months on two or three occasions, during which the equilibrium position was not good, for the curves had shown a jumping motion ; otherwise it has answered almost as well as the bifilar, notably in the three or four last years, where the coefficient of temperature is very much reduced by the adop- tion of a contrivance to compensate the effects of temperature. Our photographs already embrace twenty-one complete years. The meteorological work, and the care connected with the administration of the observatory and the meteorological stations absorb the greater jiart of our time. The reductions of the magnetic observations are very much behind, and it would be difficult to advance simultaneously all the elements as they should be ; therefore I think that it would be convenient to establish an agreement upon the work which by preference it is de- sirable to accomplish, and for what period for a general comparison. With regard to No. 7 of the suggestions of Sir J. H. Lefroy, I am en- tirely of his opinion, and I will add my ideas upon some researches that I think would throw light upon the causes of the disturbances. 1. In a paper by Messrs. Capello and B. Stewart (' Proc. R. S.,' January 28, 1864;) upon a first comparison of the disturbances at Kew and at Lisbon, we have recognised that of the little and abrupt disturbances of three to five minutes' duration (which are called peaks and hollows), and which are seen simultaneously in the three curves, those of the decli- nation and of the vertical force are in the same direction at Kew and in the contrary direction at Lisbon ; that is to say, while tho north end of the declination needle at Lisbon goes towards east the same end of the vertical-force instrument dips. The contrary happens at Kew, the north end of the declination needle going towards east, while the same end of the vertical-force raises itself. Again, on the other hand, we have also recognised the agreement of the behaviour of the peaks and hollows of the declination curves at Kew and at Lisbon. Thus one vertical peak at Lisbon corresponds always to a hollow at Kew, and vice versa. It would be interesting (1) to extend this research upon peaks and hollows further ; that is to say, between more distant observatories, employing the utmost rigour possible in the time-measures, in order to recognise if the times of the appearances of the peaks are absolutely the same, or if there is a sensible difference in the most distant observatories. (2) Again, we ought to look in some observatory immediately between Lisbon and Kew in order to see if the vertical-force peaks correspond sometimes to the peaks, sometimes to the hollows of the declination. 2. For the study of the disturbances I think it would be necessary that each observatory furnished with magnetographs should make pro- 78 KEPOET — 1885. jections upon tbe plaue perpendicular to the inclination-needle, of the movement during tbe disturbance of tbe dipping pole of sucb a needle supposed to be suspended without friction by its centre of gravity. ^ This projection ought to be constructed by means of the declination variations ( A<i) and those of the inclination (At) ; the first being multi- plied by the cosine of the inclination (cos /), in order to its reduction in the inclination direction. The readings of the thi-ee curves being made at the time of the first meridian, chosen at intervals of 2 m., 3 m., or 5 m., according to the deo-ree of precision which is desired, their differences are taken by com- parison with the first reading, and these differences should be reduced according to the values of the coefBcients. In combining the values of the movements of the vertical force and of the bifilar, we find by the known formula (^ At=3in icosiY -^ _ -^ j J the variations of the incli- nation ; these variations are projected upon the chart in vertical directions, havino' reference to the first reading, and those of the declination in horizontal directions, employing a convenient scale. Here is an example: — Four hours of the disturbance of the 1st of February, 1881, Oh. to 4 h. (time of Pawlowsk) at Kew, and Lisbon readings being at the intervals of five minutes. It is noticed that all the movements are reproduced in the two figures. They are generally at great length, and now and then deformed at Kew and of different inclination by comparison with the horizontal line. All the movements at Lisbon and Kew are executed in the manner con- ti'ary to the hands of a watch. The aspect is sooner at Kew. If Ave make a similar research upon other more distant observatories — for example, Pawlowsk and Toronto — the same movements are still re- marked ; but some aspects are completely deformed, the movements at Toronto being executed in the manner of the hands of a watch. The measurements in these researches have been taken from the curves of a scheme of a study of Mr. Wild upon the disturbances of February 1, 1881. VII. Observations on Magnetic Reductions. By Dr. H. Wild. As Messrs. Balfour Stewart and Brito Capelloin the ' Suggestions for the Committee on Magnctical Reductions,' as well as Herr T. P. van der Stok in the ' Communications of the International Polar Commission,' No. 109, have clearly shown, there are to be distinguished in the varia- tions of the magnetic elements — 1st, their normal daily periods ; 2nd, the slow and constant changes which the absolute values of the days' means of these show ; 3rd, the eventually different daily periods which • I think that it would be possible to construct a very simple instrument which could well register b)- photography all such disturbances, which would make these researches less laborious, avoiding all the measures and reductions which are alwaj's laborious. Let a little needle be suspended conveniently by the centre of gravity, employing a thread of silk. In one point of this needle let there be a mirror per- pendicular to its magnetic axis. A luminous slit might be made to fall almost perpendicularly upon the mirror, registering the movement in all the directions of the needle. In order that these movements should not be confounded and super- posed, the registering cylinder should proceed by jerks from hour to hour, or of tener according to experience. ON COMPARINa AND KEDUCINa MAGNETIC OBSERVATIONS. 79 the deviations from the normal daily path show.' In how far we are to conceive of the two last variations as disturbances must, in my opinion, be decided by experience. In any case we require, for the fixing and estimation of these last varia- tions, a distinct starting point, which the normal daily path may present. It is, therefore, specially important here to establish this normal daily path of the magnetic elements. Now regarding the method which Sabine has devised for this, and also used so much, there is, in the first place, displayed what Lefroy, Weyprecht, and others have made so prominent, the arbitrary nature of the limits which are assumed for the expulsion of the so called disturbed data. Among the different proposals which have been made for a rational fixing to these limits the most worthy of notice is that of Buys Ballot, in which these limits are to be set where the devia- tions begin to show another period. Van der Stok has distinctly modified the Sabine method for the discovery of the normal daily path. His altogether very complicated method suffers, in my opinion, from the same wide evils as the Sabine method, viz., that it proceeds from the daily paths, derived, like them, from the sum of all observations without dis- tinction, i.e. including disturbances. Now it is evidently, as Weyprecht has already shown, impossible out of the so procured data to get rid alto- gether of the influence of the disturbances on the normal daily path, if these are not quite irregularly distributed over the day, but are all subject to a certain daily period. Lefroy again, in his working out of observations at Tort Simpson and Lake Athabasca, has not employed all the data for the deriving of the first hour's means, but only the days and hours which, according to him, wei-e not to be regarded as disturbed, i.e. where the amplitude of the movements does not go beyond a certain limit. The fact that the exclusion of these movements is not settled through the criterion of Buys Ballot on the one hand, as well as the consideration, on the other, that days with not less amplitude of movement may also be disturbed, because the disturbed periods might unite with the normal periods, so as to weaken themselves through interference (which, as we shall see, is partly the case), prevents the method from being satisfactory. In the Programme and in the Sittings of the fourth International Polar Conference in Vienna (April 1884) I have given out and developed a new method for the derivation of the normal daily path of the magnetic elements (see ' Communications of the International Polar Commission,' No. 94, p. 199 ; No. 97, pp. 208, 211 ; No. 98, pp. 254, 255, 257, 258), ■which is supported by the observation that in the magnetograph traces, even at the epoch of maximum disturbances, in every month are to be found a number of days in which a quite regular, and also as regards these days concerned a recurring periodical path is distinctly recognised. I regard these days as days with undisturbed daily paths, and the hourly means of all these days as representative of the normal daily path of the elements concerned in the month in question, according to its relative as well as to its absolute size. The selection of these normal days may from the first likewise seem very arbitrary ; in practice, however, this is not the case, as hardly a doubt can arise as to which days are to be taken, and besides the result will not be very distinctly different whether one chooses one or two days more or less, if from the first one 'For the sake of simplicity I have spoken here only of the daily periods ; clearly for the remaining periods also, which show the variations of the earth's magnetism, suitable distinctions can be made. 80 REPORT — 1885. only takes the precaution to eliminate through linear interpolation any sudden and individual disturbances which in such days at times show themselves. The differences of all the observed data from the so obtained values of the normal daily path in each month I regard as deviations from the normal, eiSected by some disturbing circumstances. Should, e.g., all these deviations for all hours' values be put in the form of a table, and should each be distinguished as positive and negative, either by certain signs or, according to Balfour Stewart, by different colours, we should recognise at once, from the similarity of the signs and the nearly similar size of the figures, whether a day was disturbed uni- formly positive and negative, and from the recurrence of the positive figures at certain hours, and negative in certain other hours on different days, whether the disturbance points to a new period different from the normal daily periods. In order to establish these conclusions with numerical correctness, it is best to group the deviations according to their extent, separating negative and positive, and then to investigate their periodicity as Buys Ballot has proposed. Herr D. Miiller has worked out according to these principles the jottings of the magnetogi'aph in the Observatory of Pawlowsk for the period of the International Polar Expedition, August 1882 to August 1883. His important results have been laid by me befoi'e the Imperial Academy of Science, May 21 and June 2, 1885, and are at present published in the ' Repertoriura for Meteorology.' Without entering into the details of Herr Miiller's results, I only remark that the success of the first attempt seems to speak well for this method. The course of the contained normal daily path in the separate months has unexpectedly become regular for all three elements — declination, horizontal and vertical intensity, and also for inclination and total intensity. The days' means of the normal days show proportionally small differences, and only the greater devia- tions have a pronounced different periodicity, which again is different for the positive and negative. Herr Miiller has therefore only pointed out the latter as disturbances, and the former as simple oscillations about the normal path. For two months, October 1882 and March 1883, I have prepared a compai'ison of Sabine's method for the declination with that got by Miiller from my method. Here, in the calculation according to Sabine, + 2 is assumed as the limiting value for the expulsion of dis- turbances ; and these operations for individual hours were repeated as often as eight times. In spite of this, there is shown by a glance at the enclosed table that even by the Sabine method the influence of the pre- vaihng positive disturbances late in the forenoon, and of the maximum of the negative disturbances in the afternoon, could not be eliminated from the result. I have the intention to get worked out according to this new method, which, in short, is applicable to all these data, certain traces of magnetographs in St. Petersburg and later in Pawlowsk from 1870, and have for this purpose for the whole period chosen the normal days out of the photograms. From this came the unexpected result that the number of these at the time of the minimum of the sun spots is not so much greater than at the time of the maximum. ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 81 3 ^^ fi O ^ p ^^ o Ti o o' ^ .^ .?- cj:. o <u *-;* »4 t^ e3 o 1885. ^ .^ r— ' r- .3 .-J •^ .^ r3 r3 > rt-3 ^ J. ceTJ " J. rt ^3 "cj "^ W •5-5 c Si i?-i a £^ i^ -? 7^ g^ 5^ S:3 P ^ s^ ^>3 S = ia.~ i? St3 ^ ? j; 3 te ^ ^ S< ^ Q 5^3 £5 P ;g !g P « CO r-( ^ -7* 1— ■^ CO CO CO ^ 1! 1 CO 1 CO CO 1 „ la CO CO ^ la N b- CM '^ ^ ■^ i -T- CO 7 CO CO 1 t- ^ t^ t^ Ml "^ ^ t^ C5 a^ t'- (M ■^ -^ ■^ 1 CO I •7^ CO 1 _ Cl Oi r? c» CO ^ CS C-1 '^ ! CO 1 CO 1 O —I O r-l i-i CO t-i C-» t- t^ Cl f-( c-j ■-' o •-5 3 '-' ■* ■* "^ 1 '^ ■* •^ 1 'Ti ■v I . b- 10 cs cs « CO I^ -^ CO CO - co LO CO 1 CI CO M* 1 1.0 ■^ '^ 1 _ ^ CO CO •^ CO CI to CO ^ CO 7 CO -1* 1 10 1 QO U3 t* (M l^ w ■a r-» CO CO !§ CO .-H 1 i-O ■^ U3 + -7< l^ "^ 1 _ c» t'- 1.0 01 -, ^ CO CO b- -f - + 00 00 + + CO (71 CO -^ CO CO CO w -* CO 00 QO — 1 CO 00 ■3- ■x> + CO 00 1 lis 00 M* to b- Ci 7 CO b- 4- CO QO do CO 1 i-H CO T*» 00 w "^ CO ^ CO <N ^ 00 CO 1 CO 10 + CO b- + CO t- t^ U3 irS ■*}• CO I— CO + CO CO M 'V + O r-* "^ ■^ Tj' 1 T|( CO CO + ^ TJ* + ^ a r~\ t^ b- l>. i-O CO CO t- CO ■^ 1 CO CO cs CO + + ■^ 00 w ^ b- l«l b- C4 t- CO ^ co CO CI c-i + ■* I '«J< l-H 1 CO f-H ■^ '^ '* 1 ■<J^ ■* -'Jl ■^ -^ 1 <f r-t CO Tf< CN « CO CO CO ■M CO ^ 1 tH 6 t CO g I CO c-i ^ ^ -1* t- CO '«»< CO ^ ^ CO en 5: •^ '"4* + '* ffl C1 1 CO CO 1 cs Tft ^ CO c^ t>- CO l-< CO UO M M ■^ •^ ■^ -•J* + C-l s C-1 + CO CO 82 REPOEX — 1885. VIII. Letter from Sir Frederich Evans to Professor Steivart. 21 Dawson Place, Bayswater, London, W. r Mai/ 0, 1883. Dear Professor Balfour Stewart, — I stall be glad to render the Magnetic Committee all the assistance in my power, but I have been much out of sorts in my health for some time, and cannot so well undertake any work requiring much application. On Tuesday I leave London for a few days, and will take the papers with me you forwarded on the 6th instant. Until we see our way more clearly, it is the discussion of the dis- turbances of the Declination needle which appears to me the most im- portant to break ground upon. On a clear insight of the probable laws at a few selected stations in both hemispheres, a discussion of other elements might well follow. Too grand a scheme and complicated methods of research would, I fear, break down. Sabine's methods had, at least, simplicity to recommend them. A letter to the above address will reach me. Yours faithfully, Fredk. Jno. Evats^s. IX. Letter from the Astronomer Eoyal to Professor Stewart. Royal Observatory, Greenwich, London, S.E. : Jtili/ 8. Dear Prof. Stewart, — The printed suggestions for the Committee on Magnetical Reductions arrived at a very busy time, and since then I have been away fi-om home ; hence the delay. As there is some diflBculty in discussing abstract questions, I think it would save misunderstanding if you would make your suggestions with reference to our Magnetical Results for 1883, now in the press, of which I send you a copy. There are several additions and alterations which I have introduced in consultation with Mr. Ellis, in order to give as much information as practicable about the magnetic curves. We now give, in addition to mean values of the magnetic elements for each day and the mean diurnal curves for each month, the daily range, i.e., the amplitude of the diurnal curve for each day, and particulars of all disturbances, small as well as large (either in the notes or in the plates). Harmonic analysis also has been applied to the diurnal variations for each month and for the year. Now the question is, how far the suggestions of the Committee are carried out in the results given. As for rejection of disturbances, I am inclined to agree with Sir Henry Lefroy in his objection to Sabine's mode of treatment. At Greenwich the practice has been to draw a pencil curve smoothing down the irregularities of the trace, and to reject as disturbed those days for which a continuoiis pencil curve, agreeing gene- rally in form with the normal curve, could not be drawn through the trace. I see no reason to modify this. Yours very truly, W. H. M. Chkistie. ON COMPARING AND KEDUCINa MAGNETIC OBSERVATIONS. 83 X. Letter from George M. Whipple, Esq., to Professor Stewart. Kew Observatory : Juli/ 29, 1885. Dear Prof. Stewart, — I have carefully read the paper you were so good as to forward to me, ' Suggestions for the Committee on Magnetical Reductions,' and must confess that I am in most points fully in accord- ance with Sir H. Lefroy. I would much rather trust to the solution of the various problems of Terrestrial Magnetism by a farther and more extended series of com- parison of curves than by an extension of numerical processes. The reduction of the Fort Rae observation shows how enormously large and frequent the variations may be in some parts of the earth ; and such being the case, I fail to see how any nseful purpose could be served by the repetition of the calculations of Gauss. I think that magneticians should endeavour, if possible, to enter into communication with geologists and seismologists, and endeavour to trace out clearly the causes of (what I would term^) superficial variations, pro- bably due, Prof. Schuster says, to electric currents, for localities well furnished with magnetic obrscrvatories, such as Europe, rather than to attempt at once to solve the whole problem of distribution throughout the earth of magnetic matter. I am, yours faithfully, G. M. Whipple, Superintendent. P.S. — I enclose also copy of some remarks addressed by Capt. Dawson and myself to the Vienna Congress on the subject. Further and additional remarlis on the questions to he submitted to the Vienna International Polar Conference. We are of opinion that careful inspection of the observations them- selves will suffice to show the days and hours when the diurnal curve follows its normal course. From days and hours selected by this inspec- tion, mean curves may be obtained, and nltimately by interpolation a series of hourly values may be arrived at for every day in the year. Readings differing from these values by more than a certain separat- ing value should be set aside and discussed as disturbances. It appeal's to us probable that the principle of determining the mean monthly diurnal curves for each station from observations selected only on such days as are shown by evidence of magnetographs elsewhere to have been mag- netically calm, assumes beforehand a uniformity of magnetic conditions over the globe, and might, therefore, fail at certain stations. A rough comparison of Port Rae and Kew Observatory results indicates to us that it is rather more advisable to deal with hours and not with days as a whole, and that therefore some rule, either Sabine's or Lloyd's, must of necessity be adopted. There seems no objection to the application, first, of Lloyd's rule to throw out disturbances, and then to the subsequent classification of these disturbances after the method suggested by Wild. We fail to see as yet any method of introducing possible corrections for sun-spot periodicity into observations made during so short an inter- val of time at stations where no previous observations have been taken ; and therefore recommend that this disturbing element be omitted entirely 84 REPORT — 1885. fi'ora the proposed international discussion, and left entirely to specialists for subsequent treatment. With regard to the discussion of disturbances, we would suggest that each expedition should draw up a list of the days, selected according to Gcittingen time, considered by them a disturbed day, and then from a comparison of such lists the Conference should decide on what days should be selected for particular discussion in addition to the term days. Question 3. — Dr. Wild's suggestion as to plotting the curves is so very convenient that we have already adopted it in making preliminary curves of the Fort Rae observations. It will be necessary in addition, however, to decide upon the scale of abscissa} to be used for the 2U- secoud interval observations on term hours. We suggest the employment of a scale giving six minutes of abscissaj to each minute of time. Questions 4 and 5. — The conversion of Gaussian units into those of the C.G.S. system is so simple that it is unnecessary for the Conference to disturb the existing historic system. The Kew Observatory has already for years published their results in both systems. The foot-grain system is rapidly becoming obsolete, most magnetometers now constructed having metre instead of foot scales. XI. Letter from General Lefroy to Professor Stewart. 82 Queen's Gate, S.W. : Jiili/ 15, 1885. My dear Professor, — I have carefully read, and return herewith, the papers of Senhor Capello and Dr. Wild. I have difficulty in attaching a physical idea to the ingenious method of projection proposed by Senhor Capello. He gives the movement, projected on a plane perpendicular to the dip of the axis or intersection of the plane of dip and the plane of declination ; but I do not see how the variations of total force are to be shown in conjunction with this, or with what physical notions to connect the resulting curves. The actual realisation of the suspension of a needle by its centre of gravity without friction in any direction, especi- ally if counterpoised to carry a mirror, would be a great achievement, b'at, with great respect, I doubt its being possible. Still his comparison of Lisbon and Pawlowsk is very curious, and strongly conflrms my belief that, be our stations few or many, the results at all of them must be brought into one view, by identity of treatment and prompt circulation, to obtain a clue, and to effect this we want a Bens ex machina. My file of bulletins of the International Polar Commission does not go beyond Part 5. I have not seen Herr van der Stok's communication, which Dr. Wild refers to. It has occurred to rae, following a hint of Lloyd's,' that the area of movements would be a good measure of the forces pro- ducing them, and that it might be possible by an instrument on the prin- ciple of Amsler's planlmeter to integrate these areas for the whole twenty-four hours, or any not very small portions of it, in moderate dis- turbances. The extremely active ones would not be easily measurable. To take cognisance, as has sometimes been done, of those movements only which coincide with hours of mean time or Gottingen time, appears to me to forego the special advantages of continuous recoi'd. I agree with Dr. Wild that there is no difficulty in selecting the normal days at ' Trans. R.I.A., vol. xxii. ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 85 any station, but whether they -woulcl be the same at other stations has not, as far as I know, been ascertained. Lloyd, as you know, worked out the consequences of adopting every possible value of disturbance test. Sabine has given two or three values, all purely empirical. If my plan of areas were practically feasible, it does seem to me free from that ob- jection. Dr. Wild appears to disregard magnitude, and to refer all the observed data to his normal values, and I think nothing less comprehen- sive will be found satisfactory in the long run. It is gratifying, however, to find that his results are not widely different from those obtained by Sabine's method. As Dr. Wild quotes Toronto, I suppose that some hmited circulation and occasional comparison does go on, but Carpmael has no staff to keep it up regularly. We all want more hands, which means more money. Believe me faithfully yours, J. H. Lekrot. XII. Observations, S,c. By Chakles Chambers, F.R.S.. Superintendent, Colaba Observatory, Bombay. There can be little doubt that the activity displayed during the last quarter of a century in the record of the phenomena of terrestrial mag- netism was induced mainly by the interesting results to which Sabine was led in his discussions of the observations of the British, colonial, and other observatories ; that it was in the hope of extending and completing such results by wider observation, that men of science in all parts of the civilised world urged upon their respective Governments the advisability of establishing magnetical observatories. Few who have studied Sabine's memoirs — displaying, amongst other remarkable generalisations, the out- lines of a system of the globe in respect of the regular solar diurnal variations and the variations of these with the season of the year, and connecting with the sun-spot period variations of the range of the regular diurnal variation of declination and of the aggregate amounts of dis- turbance — will doubt the wisdom of the influence thus brought to bear on the guardians of the public purse, nor, whatever else may be done, of the propriety of carrying the work to the legitimate conclusion of extend- ing and completing Sabine's results. To act otherwise, in the absence of a physical theory to which there is as yet no clue, would be to admit a change of judgment which there is nothing in the circumstances of the present day, any more than there was at the time when the work of auto- matic registration was initiated, to justify, and would, moreover, be to discourage the statesmen who, by the provision of funds, have aided in the production of records of the crude phenomena, from making farther sacrifices in that direction : these dignitaries would, in their capacity of trustees for society, rightly complain that they had been led to expect systematised knowledge, but had been given instead piles of records of unused facts, and that the responsibility and expense of preserving these is scarcely a substitute for the reward they had been dazzled with the promise of. 2. In my opinion the scientific authorities, on whose advice much money has been spent in procuring many years' continuous records, are bound in honour to see that the representations which induced the various Governments to provide funds are justified by at least a full carrying out 86 REPORT — 1885. of tlie original purposes as to tlie uses to which the records were to be applied. 3. The fact is that funds have been expended too exclusively upon material appHances, and upon agency for working them : the statesman can understand that his country gets a tangible return when observa,tory buildings, instruments, operators, records, and reports appear before him as a result of the grants that he makes ; but it is for the man of science, the original adviser, to make him understand that these are very delusive results unless supplemented by appropriate measurement, computation, and discussion. 4. And this is the more important inasmuch as the cost of utilising the records, even up to the point suggested by Sabine's examples, will at least equal the amount that has been expended in their production. It is indispensable that inexpensive measuring, copying, and computing power should be used, under skilled direction, on a large scale ; and here it is that the main part of the cost arises. It would be simple waste of superior energy to set a cultivated physicist to the appalling task of per- forming the simple but multitudinous series of operations thatai-e involved in any adequate treatment of the observations ; and it is to the insufficiency of suitable agency in the working power of existing observatories that is probably to be attributed the fact that so little has yet been done in the way of independent reduction and discussion of the records of the auto- matic magnetic instruments. That the work before us is laborious and costly is, however, no argument against the undertaking of it if we have reason to believe that an adequate return will be obtained ; and a more costly process is to be preferred to a less costly one if the quality of the results that are the outcome of it is higher in a corresponding degree. 5. I cannot but think that the wonderful progress made during the last century in the experimental sciences is apt to make us unduly im- patient of the necessarily slower progress of the observational sciences. If astronomy had, during the progress of observation, to have its period of phenomenal generalisation — its Ptolemy, its Copernicus, its Kepler— before light as to the mode of physical causation dawned upon its Newton, is it much to be wondered at that a much more complicated science, as terrestrial magnetism undoubtedly is, should have to pass through its period of discoveiy of general phenomenal relations — relations which the physical theory will ultimately have to explain — before the conditions essential to the conception of a general theory can be laid down ? 6. It will be seen that whilst I have no faith in the flights of genius that would look at the crude facts as nature presents them to us, and from such comj^lex data devise a theory to unravel the complexity, I have the greatest confidence in appropriate methods of analysation as leading to relatively simple jDhenomenal generalisations, and thence, inevitably in the long run, to the desired physical theory. The first step to be taken should, I think, be to collect together all accessible results that have already been worked out and published of the nature of — (1) The regular solar-diurnal variations; (2) The disturbance variations — diurnal, annual, and secular ; and (3) The lunar-diurnal variations ; and to convert the expression of them for each of the elements, declination, horizontal force, and vertical force, as far as available, into metre-gramme- second or C.G.S. units of force. If not already done, the averages of ON COMPABINa AND EEDUCINa MAGNETIC OBSERVATIONS. 87 {1) should be calculated for each month from the separate results of all the years that are available, and curves be constructed to represent these average monthly variations according to time-scales and force-scales which would be marked on the curve-forms. It would be convenient that the curves should appear, for any one station, in a row, beginning with January, on a long narrow slip of thick paper, so that the sets of curves for any one station might be placed close under those of any other station for easy comparison. For preservation, the slips of paper would be kept in a portfolio, not bound into a book. Curves on a less elaborate scale, as would be suggested by the meagreness (or fulness) of the materials collected, might similarly be constructed on slips to represent the variations (2) and (3). Such series of curves, to the extent to which data for them would be found easily accessible, would, I imagine, con- stitute a conclusive answer to those who doubt the utility of extending investigation in the same direction ; but, taking continuity of change of character of the variations in passing from place to place as a criterion of the value and importance of the results obtained, they would also serve the further purpose of suggesting whether and where Sabine's methods are exact enough, or to what extent the application of even more laborious processes of reduction would be justified. These curves should be lithographed on thick slips of paper, and distributed amongst the directors of observatories and other students of terrestrial magnetism ; and, as little in the shape of description or comment need accompany them, the originals could be produced by agency of an order that should be readily obtainable, and that would require but little supervision, from some specialist member of the Committee. The curves might, with advantage, be accompanied by a table of the absolute values of the elements declination, horizontal foi'ce, and vertical force for each station ; and also by tables of ranges of the solar-diurnal variations of each element on the average of each full year. 7. It has been well established by Broun and myself that the so-called lunar-diurnal A^ariation is a function both of the season of the year and of the age of the moon, and there is reason for believing that the bulk of the phenomena is really a part of the regular solar-diurnal variation, a part that reverses its character four times in the course of the lunation. Now the adoption, by Sabine's process, of a uniform solar-diurnal variation for the whole of a calendar month, whilst perhaps accurate enough for the determination of the general character of the disturbance laws, leaves much to be desired when the object we are in quest of is a minute variation which has, in the case of the declination, a less range than a single minute of arc, and which is subject to variation of character with change of season. Here we require that a mean solar-diurnal variation should be calculated for each individual day, in order that the elimination of mean solar effect should be nearly complete ; and knowing that either a part of the solar-diurnal variation, or the bulk of the lunar- diurnal variation, runs through a cycle of change in a lunation, the best period for which to calculate the daily means is a mean lunation, or the nearest odd number of mean solar days to a mean lunation — that is to say, twenty-nine days. The importance of this period should be kept in view from the first, whether or not there is any immediate purpose of investi- gating the lanar-diurnal variations, and my present object is not so much to advocate the inclusion of such investigations in the first general scheme of operations as to explain why the period of twenty-nine days 88 REPORT — 1885. enters into modiScations that I would suggest of tlie procedure proposed by Dr. Balfour Stewart in dealing witli the horizontal force tabulations, Taut whicb modified process should, I think, be applied also to the de- clination tabulations. It is not a general rule that the hours at which the bulk of disturb- ance occurs are the same for both the elements declination and hori- zontal force ; and hence — thougb it is liighlj probable that distui-bance of some degree in one element occurs on the same day as disturbance of another degree in the other — we cannot with safety allot the disturbances to identical hours. 8. First, I would substitute for Sabine's classification of disturbances as 'larger' and 'smaller,' a division into tho.se that ai'e without the limits set by the normal ± the separating value, and those that are within those limits ; and instead of rejecting disturbed observations I would, at such step of Sabine's process for separating the larger dis- turbances, replace each disturbed entry by the same number minus the disturbance without the limits — as apparent at that stage. The dis- turbances without the limits would be separated and the laws of their variations determined by the methods that Sabine applied to his larger disturbances, but the disturbances within the limits would remain in- volved with the regular variations until a late stage of the investigations. 9. Secondly, as regards jirogressive change in the readings, both of the declination and horizontal force instruments, it would, I think, gene- rally suffice to treat that change as uniform during the course of a month. Having entered the hourly tabulations for a given month on a table (A call it) having the hours marked at the top of the columns and the days of the month in the first or left-hand column, and having taken daily means, I M'ould take the mean of the first fifteen of those daily means and the last fifteen of the preceding nionth's table A as the mean number for the beginning of the month ; and similarly the mean number for the end of the month would be the mean of the last fifteen daily means of that month and the first fifteen of the next following month. Change at the uniform rate indicated by the mean numbers ' for the beginning and end of the month I would eliminate from the original hourly tabula- tions of table A, and enter the new number on a new table (B), to which I would proceed to apply Sabine's (modified) process. This would lead to a general knowledge of the regular solar-diurnal variations for each month, and of the laws of the disturbance variations ; and here a rest- ing-place might be found if it were desired to compare results from different stations before proceeding with more elaborate reductions. 10. To proceed, however, I would next, having obtained the amounts of disturbance without the limits, eliminate these amounts from the re- spective disturbed observations of table A, calling the table thus altered (A'), and this table should form the basis of discussion in respect of the regular solar-diurnal variations for each day, the lunar-diurnal variations, and the laws of variation of disturbances within the limits. From table (A'), and the corresponding table of the preceding and following months, I would construct another similar table (C),each entry in which would be the 29-day mean of the numbers for the same hour ' The effects of disturbances without the limits on the daily means I would take to be sufficiently indicated by the departures of those means from corresponding daily means, as calculated from the mean numbers for the beginning and end of the month, with a uniform rate of change from one to the other. ON COMPARING AND REDUCING MAGNETIC OBSERVATIONS. 89 in table (A'), viz., of the numbers for the day of the entry and the four- teen preceding and fourteen following days. The numbers of table C for all the hours of a given day we may take to represent very approxi- mately the mean solar-diurnal variation — flus a constant — for that day, the average extending over the lunation of which that day is the middle day. They will be affected by progressive change of the values of the tabulations, and by disturbance within the limits. 11. Lastly, the excesses of the numbers of table (A') over the corre- sponding numbers in table C, fJus a constant round number,^ should be entered on a fourth table (D). The numbers of this table, which will be affected only by that part of the solai'-diurnal variation which goes through a cycle of change in a lunation, and by disturbance within the limits, we may proceed to arrange in new tables with reference to the moon's age and the season (or month) of the year,^ and so determine the character of the variations which the luni-solar-diurnal variation is subject to. Having done this, a further elimination will put us in pos- session of residual numbers, the variation of which must be attributed solely to disturbances within the limits, and may be studied and the numbers be manipulated accordingly. 12. I agree with Dr. Balfour Stewart that the time has not yet arrived for laying down rules for the treatment of the vertical force tabulations. XIII. Letter frovi the Eev. Professor S. J. Ferry, F.B.S. Sej)temhcr 8, 1885. Dear Dr. Schuster, — I have read over the Report Dr. Stewart kindly forwarded, and I cannot help thinking that our first step should be to collect the results already obtained for the Daily Range of the Declina- tion, reduce the means already worked out to a common scale, and then distribute the whole in a tabular and in a graphical form. Much might be learnt from seeing these results in a collective form, and we could then better judge how far processes more laborious than those of Sir Edward Sabine are like to repay the labour. If all observations are made use of in deducing the Daily Mean Ran^e the Disturbance period will certainly interfere with the Solar Diurnal Range, and if we pick out quiet curves in which the Daily Range is well marked, we are very liable to give undue weight to variations in the Daily Range which are independent of ordinary disturbances. Yours very truly, S. J. Perry. ' The constant round number is added to avoid the inconvenience of having tO' deal afterwards vf ith jwsitive and negative numbers. - If a separate table be allotted to each day of the moon's age, the resulting mean variations will be practically the same whether the hours refer to the solar or the lunar day ; and as the numbers available are for the exact hours of the solar day, it is convenient to let the arrangement of the table be for the solar day rather than for the lunar day. 90 EEPOET — 1885. Report of the Committee, consisting of Professor Crum Brown (Secretary), j\Ir. jNIilxe Home, Mr. John Murray, and INIr. BucHAN, appointed for the purpose of co-operating with the Scottish Meteorological Society in making Meteorological Obser- vations on Ben Kevis. Dl'Ring tlie past twelve montlas the observatious on Ben Nevis have been made every honr, by night as well as by day. This remarkable continuity in the observations, conducted under such great difficulties, is due to the enthusiasm and undaunted devotion to the work evinced by Mr. Omond and his assistants, and to the completion of the Observatory building last summer with its tower, which admits of a ready egress from the Observatory when the doors are blocked with rapidly accuma- lating snow-drifts, except during those rare occasions, of which the winter months of 1884-85 afforded only one example, in the great storm of February, when from 6 p.m. of the 21st to 8 a.m. of the 22nd no light could be carried in a lantei-n outside to the instruments. This inter- ruption refei's only to the observations of the temperature of the air. During the year the most notable additions made to the observations refer to the I'ainfall and the wind. The actual precipitation — rain, sleet, snow, or hail — has been collected with rain-gauges specially designed for the purpose, and measured with the greatest care every hour since June 24, 1884, with, it is believed, a very close approximation to the truth ; and the hourly results for each month have been calculated. In the end of October the anemometers designed by Professor Chrystal for the Observatory, to register continuously the velocity and direction of the wind, were added to the observing instruments. Unfor- tunately, however, in tlie colder months of the year the deposition of ice-crystals, which Mr, Omond has described in a recent paper, renders all anemometei's quite useless, except at rare intervals. During the seven months from November 1, 1884, to May 31, 1885, there was only a mean of thirty days in which the anemometer Avas in working order. During these days the greatest velocity was on the night of April 24-25, w^hen for twelve hours the mean velocity was seventy-four miles, rising one hour to eighty-one miles. Estimations of wind-force have continued to be made every hour during the year, and the results show, as in the previous year, that the wind is above the mean daily force during the night and below it during the day. The maximum occurred from 2 to 3 a.m. and the minimum from 2 to 3 p.m., the difference between the extremes being between two and three miles an hour. The means of the observations made since the Observatory was opened show that the same relation holds good during each of the four seasons. These peculiarities in the diurnal variation in the velocity of the wind on Ben Nevis are of the greatest importance, especially in view of similar curves obtained at other high-level obser- vatories situated on mountain peaks, and by Mr. Archibald Douglas from his balloon observations and experiments, and their bearing on atmo- spheric movements. During July 1885 the anemometers have been continuously at work, and there are now before us a month's complete hourly records of recorded velocities and estimated wind-force. The curves drawn from ON METEOROLOGICAL OBSERVATIONS ON BEN NEVIS. 91 the results of these two methods are closely congruent. This double set of observations supply the data for a more exact conversion of the estimations of wind-force, according to Beaufort's scale, into their equiva- lents in miles. A large number of similar observations made on boai-d the Challenge!- also form a valuable contribution to this inquiry. So far as the observations go, they appear to indicate that the equivalents in miles usually given for the higher numbers of Beaufort's scale are too small. From 8 to 9 a.m. of August 9 the anemometer registered 86 miles, and during this hour the estimated force was from 8 to 9 of the scale. The equivalent in miles for this force, provisionally adopted by the Meteorological Council, is from 48 to 56 miles. What is the number of miles when an estimated force of 10 or 11, which has been not unfrequently recorded during the colder months of the year, is reached and maintained for some time remains to be seen. Instances will in all probability occur during the autumn before the ice-deposits of the wind practically seal up the anemometer for the winter months. The mean temperature for the year ending May 1885 was 30°-G, or 0°'3 below the calculated normal temperature given in last year's Report. The tempei'atures for the same period for stations in the more immediate neighbourhood were from 0°-3 to O''-^ below their normals, being thus identical with the deviation from the normal at the Observatory. The extremes of temperature for the year were GO°'l at 2 p.ji. August 9, and 11°T at midnight and 1 A.M. February 16, thus giving a range of 49°-0. The coldest week yet experienced was the week ending February 21, the mean of which was lG''-2. In this week the lowest temperature for the year occurred, and the humidity fell to 22. Great dryness associated with great cold scarcely ever occurs in the weather records of the Ben, and in this case the exceptionally cold dry weather terminated with the great storm of the 21st and 22nd February already referred to. From the observations of the maximum and minimum thermometers the mean daily range of temperature is — in winter, 6°'8 ; spring, 6°'4 ; summer, 7°'l ; and autumn, 6°-6 — there being thus little variation with season. From the dry bulb, there is only 0°'7 between the mean coldest and mean warmest hour of the day in winter, but in summer the diffe- rence is 3°'0. It follows that in all seasons, but particularly in winter, the changes of temperature which occur are only in a subordinate degree due to the direct influence of the sun, but are chiefly caused by the passage of cyclones and anti-cyclones over the Observatory. Indeed, it may be regarded that, in the stormy months of winter, the Ben Nevis observations present the cyclonic and anti-cyclonic changes of tempera- ture in their simple conditions, uninfluenced by the heat of the sun. Lower relative humidities were observed than during the previous year. On January 20, the mean of the twenty-four hours gave the very low mean humidity of 32. On the 15th of the same month, at 5 a.m., the dry bulb was 20°-9 and the wet 16°-2, which from Glaisher's tables indi- cates a dew-point at — 16°-2 and a humidity of 19, being respectively the lowest yet noted on the top of Ben ISTevis. The lowest temperature ever observed anywhere in the British Islands was — 16°-0, at Springwood Park, near Kelso, in December, 1879, which closely agrees with the lowest dew-point on Ben Nevis. As regards atmospheric pressure, it is only in winter that the afternoon minimum falls below the mean daily pressure ; in summer this daily minimum is 0-007 inch above the daily mean. On the top of Ben Nevis, atmospheric pressure of the three seasons, spring, 92 EEPORT — 1885. summer, and autumn, is above tlie daily mean for fifteen hours, from 10 A.M. to midnight, and below it for nine hours, from 1 to 9 A.M. In June, when the sun's heat is most powerful, the afternoon minimum is the least pronounced, and the diurnal curve of pressure tends towards a single maximum and minimum, similar to what occurs in the same months over the open sea in the higher latitudes. Except in mid-winter these seasonal peculiarities of the pressure are seen in the results of each month's obser- vations, and the regularity in the changes from month to month, in the times of occui-rence of the four phases of the pressure, is very striking. The sunshine-recorder shows 461' hours of suushine for the twelve months, which is about 11 per cent, of the possible sunshine. As regards the partition of the sunshine through the hours of the day, the most note- worthy circumstance is that daring spring, summer, and autumn the amount is very considerably greater before noon than after it. As com- pared with the afternoon, the sunshine of the forenoon is 43 per cent, greater in spring, 60 in summer, and 33 in autumn, whereas in winter the amounts are nearly equal. During summer the maximum sunshine occurs from G to 9 a.m. This diminution in suushine later in the day is no doubt caused by the ascending aerial currents which rise from the heated sides of the mountain during the warm hours of the day, and the condensation of the aqueous vapour into cloud which is the consequence. Very heavy rainfalls are of frequent occurrence on Ben Nevis. Of single hours the largest was 1'302 inch, from noon to 1 p.m. of December 10, 1884. The largest daily fall was 4'264< inches, on December 10, 1884, a fall all but equalled by that of October 25, which was 4-231 inches. A fall of at least one inch occurs, on the average, one day in seven. Combining all the rainfall observations made since June, 1881, the following are the averages ; those from July to September being for four j^ears, June and October for three years, and November to May one year only. inches inches January . . . 7-33 May .... 837 February . . 10-94 June. . . . 880 March . . . 12-89 Juh .... 1070 April . . . 485 August . . . 11-24 inches September . . 944 October . . 11-0& November . . 1930 December . . 25-20 Year, 146-14 inches. There can be little doubt that the Ben Nevis Observatory has the largest rainfall of any place in Scotland at which a rain-gauge has hitherto been observed. The observations at Fort William by Mr. Livingston, consisting of eye observations six times a day, and continuous recoi'ds of the atmo- spheric pressure and temperature by a barograph and thermograph, have been regularly carried on during the year. It is not possible to over-estimate the value of these sea-level observations at Fort William, in their relations to the observations made on the top of Ben Nevis, it being from these relations that the Ben Nevis observations have their supreme importance in discussing the great problem of the weather changes of North-western Europe. This inquiry is now being carried on under the superintendence of the Directors of the Observatory. ON THE RATE OF INCREASE OF UNDERGROUND TEMPERATURE. 93 Seventeenth Report of the Covimittee, consisting of Professor Everett, Professor Sir W. Thomson, INIr. Gr. J. Symoxs, Sir A. C. Kamsay, Dr. A. GtEIKIE, JMr. J. Gtlaisher, Mr. Pengelly, Pro- fessor Edward Hull, Professor Prestwich, Dr. C. Le Neve Foster, Professor A. S. Hersciiel, Professor Gr. A. Lebour, Mr. Galloway, ]Mr. Joseph Dickinson, Mr. G. F. Deacon, Mr. E. Wethered, and Mr. A. Strahan, appointed for the purpose of investigating the Rate of Increase of Underground Temperature dowmvards in various Localities of Dry Land and under Water. Drawn up by Professor Everett (Secretary). The present Report is for the two years wbicli have elapsed since the summer of 1883. Observations have been taken in a deep bore at Richmond, Surrey, by Mr. Collett Homersbam, M.Inst. C.E., F.G.S. It is on the premises of the Richmond Vestry Waterworks, on the right bank of the Thames, and about 33 yards from high- water mark. The surface is 17 feet above Ordnance datum. The upper part consists of a well 253 feet deep, with an internal diameter of 7 feet at top and 5 feet at bottom, which was sunk in 187G for the purpose of supplying water to the town of Richmond, and carried down to the chalk. From the bottom of the well a 24-inch bore-hole was sunk to the total depth of 434 feet, thus penetrating 181 feet into the chalk. This portion of the work was completed in 1877. Above the chalk were tertiaries, consisting of 160 feet of London clay, 60 feet of the Woolwich and Reading beds, and some underlying sands. TJie water yielded at this stage was about 160 gallons a minute, and when not depressed by pumping was able to rise 4 or 5 feet above the surface. Its ordinary level, owing to pumping, was about 130 feet lower. In 1881 the Richmond Vestry determined to carry the bore-hole to a much greater depth, and the deepening has been executed under the direction of Mr. Homersham's father, who is consulting- ensineer to the Vestry. The existing bore-hole was first enlarged and straightened, to enable a line of cast-iron pipes, with an internal diameter of 16^ inches, having the lower end driven water-tight into the chalic at a depth of 438 feet, to be carried up to the surface. The annular space surrounding this ])ipe served to furnish an uncontaminated supply of water to the town during the deepening. Tlie total thickness of the chalk was 671 feet. Below this was the upper greensand, 16 feet thick ; then the gault clay, 201^ feet thick ; then 10 feet of a sandy rock, and a thin layer of phosphatic nodules. Down to this point the new boring had yielded no water. Then followed a bed 87^ feet thick, consisting mainly of hard oolitic limestone. Two small springs of water were met with in this bed at the depths of 1,203 and 1,210 feet, the yield at the surface being 1^ gallons a minute, with power to rise in a tube and overflow 49 feet above the ground. A partial analysis of this limestone rock showed it to contain 2-4 per cent, of 94 REPORT — 1885. sulphide of iron in the form of pyrites. At the depth of 1,239 feet this limestone rock ended, and hard red sandstone was found, alternating with beds of variegated sandy marl or clay. After the depth of 1,253 feet had been attained, the yield of water steadily increased as the boring was deepened, the overflow at the surface being 2 gallons a minute at 1,254 feet, 8 gallons at 1,363 feet, and 11 gallons at 1,387 feet. It rose to the top of a tube carried 49 feet above the surface, and overflowed ; and a pi-essure-gauge showed that it had power to rise 126 feet above the surface. The diameter of the bore was 16|^ inches in the chalk, 13^ inches in the gault, llj inches in the oolitic limestone, and at the depth of 1,334 feet it was reduced to a little under 9 inches. At 1,337 feet the method of boring was changed, and instead of an annular arrangement of steel cutters, a rotary diamond rock-boring machine was employed. The bore- hole, with a diameter of 85 inches, was thus carried down to 1,367^ feet, at which depth, lining tubes having to be inserted, the diameter was re- duced to 7j inches, and this size was continued to 1,447 feet, at which depth the boring was stopped. The bore-hole was lined with strong iron tubes down to the depth of 1,364 feet ; and those portions of the tubes that are in proximity to the depths where water was struck were drilled with holes to admit the water into them. Three observations of temperature were taken at the depth of 1,337 feet, during the interval between the removal of the steel borers and the erection of the diamond boring-machine. The bore-hole was full of water, which was overflowing at the rate of from three to four gallons a minute. The thermometer employed was an inverted Negretti maximum, supplied by the secretary-. In each case the temperature re- corded was 75^° F. In the first observation, March 25, 1884, the ther- mometer was left for an hour and a quarter at the bottom of the bore-hole, and three weeks had elapsed since the water was disturbed by boring. The second observation was taken on March 31, when the thermometer was 5i hours at the bottom. In the third observation special precau- tions were taken to prevent convection. The thermometer was fixed inside a wroiight-iron tube, 5 feet long, open at bottom. The thermo- meter was near the lower end of the tube, and was suspended from a water-tight wooden plug, tightly driven into the tube. There was a space of several inches between the plug and the thermometer, and this part of the tube was pierced with numerous holes to allow the escape of any cold water which might be carried down by the tube. The tube was one of a series of hollow boring- rods used in working the diamond drill- machine. By means of these it was lowered very slowly, to avoid dis- turbance of the water as much as possible ; and the tube containing the thermometer was gradually worked through the sand at the bottom of the bore-hole. The lowering occupied five hours, and was completed at noon on Saturday, June 7. Cement, mixed with sugar, for the purpose of slow setting, was imme- diately lowered on to the surface of the sand, and above this a mixture of cement and sand, making a total thickness of 3 or 4 feet of cement plugo-ing. The thermometer was left in its place for three full days, the operation of raising being commenced at noon of Tuesday, June 10, and completed at 5 p.m. The thermometer again registered 75^° F., exactly the same as in the two previous observations which were taken without plugging. It would therefore appear that the steady upflow of water in ON THE EATE OF INCEEASE OF UNDEEGEOUJJD TEMPEEATUEE. 95 the lower part of the bore prevents any downward convection of colder water from above. The boring has since been carried to the depth of 1,447 feet, with a diameter reduced to 7^ inches, and Mr. Homersham made preparations for a final observation at the bottom with a plug consisting of a thick india-rubber disc covered with cement and saud ; but the vestry declined to incur the responsibility of having the rods lowered again for this purpose ; and as some pieces of broken lining-tube had fallen in, there would have been serious risk of jamming. Mr. Homersham accordingly contented himself with lowering the thermometer to the bottom without plugging. It remained down for six days (Febrnary 3 to 9, 1885), and gave a reading of 76^° F. The water overflowing at the surface had a tempei-ature of 59° F. To deduce the mean rate of increase downwards, we shall assume a surface temperature of 50°. This gives for the first 1,337 feet an increase of 251°, which is at the rate of 1° F. in 62-4 feet, and for the whole 1,447 feet an increase of 26J°, which is at the rate of 1° F. in 54'1 feet. These results agree well with the Kentish Town well, where Mr. Symons found in 1,100 feet an average increase of 1° in 55 feet. ]Mr. Homersham carried on a lengthened correspondence with the secretary as to the best manner of taking the observations, and the method devised by him as above described will famish a useful model for future observers. Thanks are also due to the Richmond Vestry for permission to observe, and to the contractors, Messrs. Docwra, for the loan of their apparatus. Mr. Galloway (member of the Committee) has furnished observations taken daring the sinking of a shaft to the depth of 1,272 feet in or near the Aberdare valley, Glamorganshire. The name of the place is Cwm- pennar, and the position of the shaft is on the slope on the east side of the valley, near the summit of the hill which separates it from the Merthyr valley. The mouth of the shaft is about 800 feet above sea level. Observations were taken at four different depths, 546 feet, 780 feet, 1,020 feet, and 1,272 feet, the thermometer being in each case inserted, and left for twenty-four hours, in a hole bored to the depth of 30 inches, at a distance not exceeding 2-Jy yards from the bottom of the shaft for the time being. About eight hours elapsed between the completion of the hole and the insertion of the thermometer. The strata consist mainly of shales and sandstone, with a dip of 1 in 12, and the flow of water into the shaft was about 250 gallons per hour. The first of the four observations was taken in the fireclay under the Abergorkie vein ; the second in strong * clift ' (a local name for arena ceous shale) in disturbed ground ; the third in bastard fireclay under a small rider of coal previously unknown ; the fourth in ' cHft ' ground two yards above the red coal vein, which overlies the 9-foot seam at a height of from 9 to 12 yards. The observations were taken by the manager, Mr. John Beith, and are as follow : epth in ft. 546 Temp. Fahr 56° 780 1,020 1,272 69j° 63° 66^° 96 REPORT — 1885. Comparing consecutive deptlis from 546 feet downwards, we liave the following increments of temperature : — 3i° in 234 ft., giving 1° for 67 ft. 3i° ■sl° 240 69 — showing a remarkably regular rate of increase. A comparison of the first and fourth observations gives an increase of 101° in 726 feet, which is at the rate of 1° F. in 691 feet. As the surface slopes about 1 in 5, and the pit is near the summit of a ridge, it is probable that in level ground of similar material the rate would be about 1° F. in 60 feet. As a check upon this result, we find that this rate of decrease reck- oned upwards from the smallest depth (546 feet) would give a surface temperature of (56 — 7-9 =) 48°-l, which, as the elevation is 800 feet, is probably very near the truth. Mr. Garside has sent an observation of temperature taken by himself in the roof of the Mersey tunnel in August 1883. The temperature was 53°, the depth below Ordnance datnm being 92 feet. A great quantity of water from the river was percolating through the sides of the tunnel. On Auo-ust 13, 1884, he verified his previous observation in Denton Collieiy (Ibth Report). The second observation was made at the same depth as the first (1,317 feet), in the same pit and level, and under the same circumstances, except that the thermometer was allowed to remain fourteen days in the hole bored for it, instead of only six hours. The temperature observed was the same as before, namely 66°. Mr. Garside has also supplemented his previous contribution to our knowledge of the surface temperature of the ground in the East Man- chester coal-field (16th Report) by two more years' results from the same observing stations. The following are the collected results, includ- ing the year previously given : — Croft House, in the centre of AsJdmi-under-Ljjne, 345 ft. above sea. I — 4 ft. Deep 1 ft. Deep Mean of Max. and Min. Air 1882 1883 1884 47°-5 46° G 4S°-3 46°-2 45°-o 47°-3 48°-4 47°-8 48°-9 Means 47°-5 46°-3 48°-4 District Ivfirmary, 501 ft. above sea. — 4 ft. Deep 1 ft. Deep Mean of Max. and Min. Air 1882 1883 1884 45°-9 46°-3 470.7 4.5°-6 45°-3 47° 3 46°-6 46°-3 48°-2 Means 4€°-6 46°1 47°0 Giving equal weight to the 4-foot and 1-foot observations, we have a mean surface temperature of 46°-9 at an elevation of 345 feet, and 46°-4 ON THE EATK OF INCIIEASE OF 0x\DERGKODND TEMPEllATUUK. i>7 at 501 feet. The diBFerence between them agrees well with the generally accepted rate of 1° for 300 feet, and indicates about 48° as the surface terapsrature at small elevations, such as 30 feet. The pits in the East Manchester coal-field from which we have observations, namely, Astley Pit (Uakinfield), Ashton Moss, Bredbury, Denton, and Nook Pit, are all sunk in ground at elevations of between 300 and 350 feet. It would therefore appear that the assumption of a surface temperature of 49°, which wc made in reducing these observations, is about 2° in excess of the truth. A very elaborate paper on Underground Temperature has recently been communicated to the Royal Society by one of the members of the Committee — Professor Prestwich. It contains probably the fullest col- lection that has ever been made of observations of underground tempera- ture, accompanied iu most cases by critical remarks ; and adduces arguments to show that most of the temperatures observed are too low, ■owing to the influence of the air in mines, and of convection currents in wells. Professor Prestwich is disposed to adopt 1° F. in 4-3 feet as the most probable value of the normal gradient. Report on Electrical Theories. By Professor J. J. Thomson, M.A., F.R.S. In this report I have confined myself exclusively to the considei-ation of those theories of electrical action which only profess to give mathematical ■expressions for the forces exerted by a system of currents, and which make no attempt to give any physical explanation of these forces ; for it is evident that before we can test any theory of electrical action we mu.st know what the actions are \vhich it has to explain, and we cannot do this until we have a satisfactory mathematical theory. 1 have further limited myself to the consideration of the fundamental assumptions of each theory, and have not attempted to give any account of its mathematical developments, except in so far as they lead to results capable of distin- guishing between the various theories. I have divided the theories into the following classes : — 1. Theories in which the action between elements of current is deduced by geometrical considerations combined with assumptions which are not explicitly, at any rate, founded on the principle of the Couservatioii of Energy. This class includes the theoi'ies of Ampere, Grassmann, Stefan, and Kortewee. 2. Theories which explain the action of currents by assuming that the forces between electrified bodies depend upon the velocities and accele- rations of the bodies. This class includes the theories of Gauss, Weber, Riemann, and Clausius. 3. Theories which are based upon dynamical considerations, but which neglect the action of the dielectric. This class contains F. E. Neumann's potential theory and v. -Helmholtz's extension of it. 4. C. Neumann's theory. 1.88.5. H 98 REPOET — 1885. 5. Theories which are based upon dynamical considerations, and which; take into account the action of the dielectric. This class includes the theories of Maxwell and v. Helmholtz. We shall now proceed to the detailed consideration of these theories. Theories in which the action between elements of current is deduced hy geometrical considerations combined with certain assumptions which are not e.rplicitly, at any rate, foutuled on the Principle of the Conser- vation of Energy. The best known theory of this class is that of Ampere. Others, however, have been given by Grassmann, Stefan, and Korteweg, which we shall consider in order. Am,pere's Theory. This theory was first published in 1820. In 1823 appeared his great paper, the ' Memoire sur la Theorie Mathematique des Phenomenes Electro-dynaraiques,' Memoires de VInstitut, t. vi., which Maxwell de- scribes as ' perfect in form and unassailable in accuracy,' and which at once brought the action between electric currents under the power of mathematics. Ampere founded his theory on certain postulates which he attempted to establish by experiment ; inasmuch, however, as he always dealt with closed circuits in his experiments and elements of circuit in his postulates, the experimental evidence is not quite satis- factory. Ampere's experiments have been repeated by v. Ettingshausen ^ with much more delicate apparatus. The postulates used by Ampere are as follows. The first four are given in the words of Professor Tait : — ^ I. ' Equal and opjoosite currents in the same conductor produce equal and opposite effects on other conductors ; whence it follows that an element of one current has no effect on an element of another which lies in the plane bisecting the former at right angles.' II. ' The effect of a conductor bent or twisted in any manner is equivalent to that of a straight one, provided that the two are traversed by equal currents and the former nearly coincides with the latter.' III. ' No closed circuit can set in motion an element of a circular conductor about an axis through the centi-e of the circle and perpendicular to its plane.' lY. ' In similar systems traversed by equal currents the forces are equal.' Y. ' The action between two elements of current is a force along the straight line joining them, and proportional to the product of the lengths of the elements and the currents flowino' through them.' It follows from IV. that the force between two elements of current varies inversely as the square of the distance between them. The assumption Y. is one that can only be justified by the correctness of the results to which it leads. We have no right to assume i^t priori that the action is equivalent to a single force, and not to a force and a couple : and we have no more right to assume that the force is along the line joining the elements than we have to assume that the force between ' ' Ueber Ampere's elektrodynamische Funclamentalversuche,' Wicn. Ber, (11), 77,. p. 109, 1878. - Tait's Quaternion?, 2nd edit. p. 249. ON ELECTRICAL THEORIES. 99 two small magnets is along the line joining their centres, and in this case the assumption is untrue. It is in the nature of the assumption V. that Ampere's theory differs from others of this class. The second part of T. depends upon V. It is not true unless we assume that the force between two elements is along the line joining them. Ampere deduces the force between two elements of current from these principles in the following way : — Suppose we have two elements of current of lengths dsi, ds^ traversed by cui-rents of strengths i, j respectively. Let us take the line joining the centres of these currents as the axis of x ; let the plane of c?s, and x be taken as the plane of xy ; let 0,, 6^ be the angles which cZs,, ds^ respectively make with the axis of x, rj the angle which the plane through tZs., and ;• makes with the plane of xy. By Ampere's second pi'oposition the action of ds^ on ds.2 will be the sum of the action of f fZ^i cos d^ or a, along x \ d'*i sin ^1 or /3i along y on ds^ cos 02 01* "2 along x ds2 sin 02 t'os V or ft^ along y ds2 sin 02 sin ?/ or yg along z. Now by proposition I. «[ cannot exert a force on either /Sg or 72* because it is in planes which bisect /j, and y.y at right angles, so that the only component on which a-^ can exert a force is u^. Let the force between these components be a -2-«l«2- ■where r is the distance between the centres of the elementary currents. In the same way we can show that the only component on which /3, can exert any force is jo.2- I^^t the force between these two elements be ^ ,•> a r- Thus the force between the two elements ds^, ds^ is — (aai«2 + 6/3 1/3 2}, or, substituting for a^a^, r'lft-z their values : -J [a cos 0, cos 9-2 + h sin 0i sin 09 cos tj} ij f?Si cZsg. The proposition III., that the action of a closed circuit on an element of current is always at right angles to the element, leads on integration to the condition 2a + i = 0, so that the force between the two elements equals -jj {cos 01 cos 02 — 2 sin 6^ sin 00 cos t]] ijdsy ds^. IFrom this we ai'e able to find the force between any two circuits or parts of circuits- To find the force on a magnetic system, Ampere used his H 2 100 EEPORT— 1885. principle that the magnetic action of an electric current was the same as that due to a magnetic shell bounded by the circuit and magnetised to the proper intensity. In this way Ampere gave a complete theory of the action of currents upon currents and upon magnets — in fact, a complete theory of all the effects produced by a current which were known when his paper was published. It is difficult to overrate the service which Ampere's theory has rendered to the science of electrodynamics. Perhaps the best evidence of its value for practical purposes is the extreme difficulty of finding any experiment which proves that it is insufficient. In spite of this, how- ever, as a dynamical theory it is very unsatisfactory. If, as we are led to do by Ampere, we attach physical importance to elements of current, and regard them as something more than mathematical helps for calcu- lating the force between two closed circuits, then we are driven to ask, not only what is the law of force between the elements, but what is the energy possessed by a system consisting of two such elements. If we do this, and find this energy by calculating the amount of work required to pull the elements an infinite distance apart, we arrive at the conclusion that the energy must depend upon the angles which the elements make with each other and with the line joining them ; but if this is so, then the force between the elements cannot be along the line joining them, and there must in addition to this force be couples acting on the elements. For these reasons we see that Ampere's theory cannot give the complete action between two elements of current. What it does — and this for practical purposes is an advantage and not a disadvantage — is to give in most cases, instead of the complete action between two elements, that part of it which really affects the case under consideration. Before discussing cases, however, in which the terms which Ampei-e neglects might be expected to produce measurable effects, we shall, in order to compare the various theories more easily, proceed to consider other theories of the same class. Grassmann's Theory.^ The method by which Grassraann obtains his theory is very remark- able. He objects to Ampere's formula for the force between two elements of current, because it makes the force between two parallel elements change from an attraction to a repulsion when the angle which the ele- ments make with theline joining them passes through the value cos~' 2/3, and the object of his investigation is to get a law of foi^ce free from this peculiarity, and which, while giving the same result as Ampere's for closed circuits, shall yet be as simple as possible. He begins by regarding any circuit as bailt up of ' Winkelstrome,' i.e., currents flowing along the two infinite lines which form any angle. He points out that a circuit of any shape can be built up of such currents ; the circuit ahc, for example, may be regarded as built up of the ' Winkelstrome ' eaf, fbg, and gee. Grassmann proceeds to calculate by Ampere's formula the action of a ' Winkelstrom ' upon an element of current («). Since the 'Winkel- strom ' will have no action upon an element of current perpendicular to its plane, we see that it is only necessary to calculate its action upon the component (a') of a in its own plane. Grassmann does this by calcu- lating the effect due to each arm of the ' Winkelstrom ' separately. He ' Fogg. Ann. O-l, p 1, 1815 ; Crelle, 83, p. 57 ON ELECTIUCAL THEORIES. 101 finds expression for the forces along and perpendicular to a', due to an infinite rectilinear current starting from a definite point. The force of such a current along a' does not depend on the angle the current makes with the line from its end to o', so that the effects of two such currents starting from the same point and flowing in opposite directions, i.e. of a ' Winkelstrom,' will be to produce no force along o' ; thus the effect of a ' Winkelstrom ' on an element of current in its own plane will be a force at right angles to the element. The force at right angles to a' due to a rectilinear current will consist of two parts, one independent of the angle made by the current with the line joining its end to the element, the other depending upon this angle. The first part will vanish when we consider a ' Winkelstrom ' ; the second part only will produce any effect. Now Grassmann says that it will much simplify the analysis, and obviously (since any closed circuit may be built up of 'Winkelstrome ') lead, for closed circuits, to the same result as Ampere's formula, if we suppose that the law of force between elements of currents is such that the only effects produced by a rectilinear current are those which do not vanish for a ' Winkelstrom,' and hence that a straight current exerts on an element of current a force at right angles to the projection of the element on the plane containing the centre of the element and the rectilinear current, and that the magnitude of this force is ij ds' cot 2' where i is the sti*ength of the rectilinear cnnent, y the strength of the 102 KEPORT — 1885. element of current, ds' its projection on the plane through its centre containing the straight current, r the distance of the element from the end of the straight current, and o the angle which the rectihnear current makes with the line joining its extremity to the elementary- current. By taking the difference of two such rectilinear currents, Grassmann finds the action of an element (/3) of current on another element («) is a force at right angles to a', the component of a in the plane containing /3 and the middle point of a and equal to . . dads' ■ n ^3 -72- «^^ ^' where is the angle which /3 makes with r, da the length of (/3), and j the current flowing through it. The direction of the force is along AB, where A is the centre of the element (a) and B the point where the normal to a' is cut by /3 produced in the direction of the current. If we treat this theory in the same way as we did Ampere's on p. 99 by considering the action of the component a,, /3i of an element of current ds, on the components 02, /^o, 72 of another element ds.,, we see that Grassmann's theory is equivalent to supposing that a, exerts no force on a^, ft.^, or 72 ; i^l^at ft^ exerts a force A/JjUo on u^ at right angles to a.^ in the plane of xxj, and a force A/3i/32 on /32 at right angles to it, that is, along the line joining the element, and that it exerts no force on y^- .... Thus we see that Grassmann's theory :s equivalent to replacmg Ampere's assumption, that the force between two elements of current acts along the Hue joining them, by the assumption that two elements of current in the same straight line exert no force on each other. As a dynamical theory of electrodynamics, Grassmann's theory is open to the same objection as Ampere's, that it does not take into account the couples which may exist between the elements, and also to the additional objection that, according to it, the action of an element of current ds^ on another element ds.^ is not equal and opposite to the action of ds^ on dsi, so that the momentum of the two elements cZs, and ds.^ will not remain constant, and, as the theory does not take into account the sur- rounding ether, there is no way of explaining what has become of the momentum lost or gained by the elements. As a piece of geometrical analysis, however, the theory is very elegant and worthy of the author of the ' Ausdehnungslehre.' From the way in which Grassmann's theory was developed we see that between closed circuits it must give the same forces as Ampere's ; for unclosed circuits this is not the case, and Grassmann, at the end of the paper quoted above, mentions a case where the two theories would give opposite results, assuming that unclosed streams exist. Suppose we have a magnet //s and an unclosed current AB in the same plane as the magnet and passing through its middle point, then if Ampere's theory be true, the magnet will twist in one direction ; if Grassmann's, it will twist in the opposite. This depends upon the change, according to Ampere's theory, of the force between two parallel elements from attraction to repul- sion, when they make the angle with the line joining them at less than sin-' 1 / v/'3', while according to Grassmann's theory, there is no such change. ON ELECTRICAL THEORIES. 103 Stefan's Theory} This resembles Ampere's theory very closely, except that Stefan does •not make the assumption that the force between two elements of current is along the line joining them : this difference leads to the introduction of two forces which Ampere neglects. We shall use the same notation as when we discussed Ampere's theory, and consider, as before, the action of an element of current dsi on another element dso. Stefan, like Ampere, assumes that we may replace an element of current by its component, so that we have to con- sider the action of the components («,, /^i) of ds^ on the components («2) ^21 y-i) of c7S|. As in Ampere's theory, the component a, is supposed to exert a force r2 on a 2, this force by symmetry must be along the line joining the elements. a, is supposed to exert a force on ji^ equal to along the axis of y. We can see that this force may exist, for it is conceivable that it should be in the same direction as jl.2 when a, points from the middle of ds^ to the middle of ds<i, and in the opposite direction to 1^2 when ctj points in the opposite direction. Stefan assumes that a^ exerts no force on /32 parallel to the axis of z, and no force at all on 72- /jj is supposed to exert a force on uo parallel to the axis of y and equal to d -, r- We may see, by the same reasoning as we used before for the force between /J, and «2> that it is conceivable that this force may exist. /3i is supposed to exert no force on 05 parallel to the axis of z. As in Ampere's theory, /ji is supposed to exert a force on j32 equal to ^ . -, -^Pilh, this force must by symmetry be along the line joining the elements ; /3, is supposed to exert no force on 72- Thus the action of ds^ on dsg consists of a force 72 |ani«2+ ^Pi/32 j .along the line joining the elements, and a force 72 |c«i,'32 + cZ/3i"2| at right angles to this line in the plane containing dsi and r. If we take ' Stefan, Wien. Sitzungshcriclde, 59, p. 693, 1SG9. 104 REPOllT 1885. arbitrary coordinate axes and suppose that .v, y, z are the coordinates of cZs,^ a;', 2/', z' those of ds.,, then the x component of the force on ds2 due to dn^ is shown by Stefan to be equal to d '■-^''^''^^'M^^^rjr (a;' — x) d 1 dx^ d r dni r ds.2 ^ __ 1 dx dso r da. 3=1-^ + 2- cost ■with similar expressions for the force parallel to the axes of y and z. Here /, j are the currents through between the elements of current, and ')n:= 3 l" •C- ds2 respectively, £ is the angle- n=l{a-h-c + 2d} f= —^{ii — h + 2c-d] q=^[a + 2h-c-d]. We see from this expression for the force parallel to x that the last term is the only one which does not vanish when integrated round two- closed circuits of which ds, and ds^ are elements. So that the force will depend only upon // ; the value of q will depend upon the units we adopt : in Stefan's work q is put equal to —1/2. This is the only condition to be got by considering the translatory foi'ce between two circuits ; we can get another by considering the couple acting on the closed circuit, supposed rigid, of which ds^ forms a part. For the s component N of this couple Stefan finds the expression c7ii'' dy _dy^ dx N = U2fP y^x — x^y cos £ dsids2 — 1 JP 'fir c7ii'' dy _dy^ ^•'' 1 i J r \ ds^ ds^ ds2 ds^ J c?>-,. But supposing the two circuits to have a potential U cos £ p: ds■^ ds.,, we can easily see that the couple . . rr.'/'.v-.'y'y = IJ ;3 - cos £ dSidS.2 n 'llL _ ^'^\ 7 , c/s, ds, dsa ds, ' ' 1 ■ '-^ '2 1 i thus if two circuits have a potentij or substituting fovp and q their values, 2a + b + C-2d^0. If c=0 and (.7=0, as in Ampere's theory, this relation becomes 2a + b = 0, which is the same relation as Ampere deduced by finding the condition that the foi'ce due to a closed circuit on an element of current should be at right angles to the element, and Stefan has proved that on his theory the same condition leads to the equation p = q, i.e., the same condition as the one which expresses that two closed circuits have a potential. ON ELECTRICAL THEOUIES. 105 Stefan shows that, fi'om the consideration of the action of closetT. circuits on elements of other circuits or of themselves, it is impossible to get any other relation between the quantities a, b, c, d, so that we have only two relations between the quantities a, h, c, d, and thus two of them must be indeterminate. We may give any values we please to these quantities, provided the}- satisfy these two relations ; if we put c = 0, c? = we get Ampere's theory ; if or, ^ 0, c = 0, Grassmann's ; and we can get a number of other theories by giving different values to these quantities. Stefan's theory is open to the same objection as Ampere's, since it does not take into account the couples which one element may produce on another. He also limits the generality of his theory by supposing that the force between two elements of currents in one plane is in that plane. Korteicey's Theory.^ According to this theory, the forces between two elements of current are the same as in Stefan's theory ; Korteweg, however, considers in addition the couples which one element may produce on another. If we use the notation we adopted in discussing Stefan's theory, we have, considering the force on dso, a force along the line joining the elements, and a force parallel to the axis of y. In addition. to these forces, Korteweg supposes that from the action of «! on /Bj there is a couple whose axis is parallel to the axis of z equal to and from the action of «i on y^ a couple on yg whose axis is parallel to the axis of y and equal to -/ar/2; from the action of /Jj on a 2 there is a couple on a. 2 whose axis is parallel to the axis of '4 and equal to and from the action of /^i on y^ there is a couple on y., whose axis is parallel to the line joining the elements and equal to A/3,02. If we now take arbitrary co-ordinate axes, the forces on the element d,--, are the same as those given by Stefan's theory. The couples, however, are different. The component parallel to the axis of x of the couple 011 ds2 is given by the equal iuti _r2 d,2 \ ./.-, cL-^J r* ds2 ds ^'' "^^ ' Crelle, xc. p. 49, 1881. lOH EEPORT — 1885. (h + a) dr / , , s dz, , , . dij'^ \ r dsi L (li<2 "*2 J 7 / f'//' ''■s dy dz "1 ~| I (Is 2 dsi dni ds2 J J ii dsi ds2, with similar expressions for the components of couple around the axes of y and z. By making the force between two closed circuits have the same value as that given by Ampere's theory, Korteweg finds that a + 2b-d-c = - 3A2, where A is a constant quantity whose value depends upon the unit of current adopted. By making the couples produced by one closed circuit on another have the same value as that given by Ampere and the potential theory, he finds that i ('•''^0 + (iZ-^O r-c + 2A2 = 0. dr Korteweg considers that the experiments of v. Ettingshausen, quoted above, prove (1) that the force on an element of circuit produced by a closed circuit is at right angles to the element, and (2) that the couple on an element due to a closed circuit has the value given by Ampei'e's theory. The first condition gives c-h = 2A2; the second the two conditions h + g = 0. And he points out that we cannot get any more conditions by consi- dering the action between two closed circuits, or the action of a closed circuit on an element of another. It should be noticed that since, according to this theory, part of the action of one element of a circuit on another consists of a couple, the condition that the force due to a closed circuit on an element of another should be at right angles to the element is not, as in Stefan's theorj', iden- tical with the condition that the expression for the couple exerted by one closed circuit on another should be the same as that given by Ampere. This theory is valuable because it is the most general one of the class we are considering which has been published. It is the only one which takes into account the couples, and by giving special values to the quan- tities a, h, c, d,f, g, h, we can get any of the other theories of this class. ON ELECTRICAL TIIEOinES. 107 ■On the theories which explain the action of currents hij assuming that the forces beticeen two electrified bodies depend upon the velocities and ac- celerations of the bodies. According to these theories a body conveying an electric current con- tains equal quantities of positive and negative electricity, so that it will Dot exei't any ordinary electrostatic eifect : the positive electricity is sup- posed, however, to be moving differently from the negative. In some of the theories (Weber's, Gauss's, Riemann's) Fechner's hypothesis, that the electric current consists of positive electricity moving in one direction (the direction of the current), and an equal quantity of negative elec- tricity moving at the same speed in the opposite direction, is assumed ; in other theories (Clausius') only one of the electricities is supposed to move, the other remains at rest. We can see in a general way how the assumption that the forces between two electrified particles depend on the velocities and the accelerations of the particles can explain the effects produced by an electric current. Let us take first the mechanical action between two circuits A and B, and let us consider the action of an element (a) of A on an element (6) of B. We shall consider first the action of the two electricities which are flowing through a on the positive electricity which is flowing through b. Since the motion of the positive electricity in a relative to that of the positive electricity in b is not the same as the motion of the negative electricity in a relative to that of the positive in b, the forces due to the positive and negative electricities in a will not counterbalance, so that there will be a resultant force on the positive electricity in b depending on the inequality between the motion of the positive and negative electricities in a relative to that of the jjositive in b. Similarly there will be a force on the negative electricity in b depending on the in- equality between the velocities of the positive and negative electricities in a relative to that of the negative in b, and, except for special laws of force and special values of the velocities of the electricities in b, this force will not be equal and opposite to the force on the positive electi-icity in b, so that a mechanical force on b will be produced by the currents through a. Let us now consider how inductive forces can be explained by this hypothesis : let us suppose that the element a is moving, and that the element b is at rest. The velocity of the electricity in a will be the resultant of the velocity with which the electricity flows through a and the velocity of translation of a itself, so that since the velocities of flow •of the positive and negative electricities are different, the actual velocity of the positive electricity will differ in magnitude from the velocity of the negative (unless, assuming Fechner's hypothesis, the element a is moving at right angles to itself) ; thus the force due to the positive electricity in a on a unit of positive electricity at b will not be equal and opposite to that due to the negative electricity in a, and thus there will be an E.M.F. at b due to the motion of a. This explains induction due to the motion of the primary circuit. Let us now consider induction due to the variation of the intensity of the current in the primary circuit. According to all the theories there IS a force produced by a moving electrified body proportional to the first power of the acceleration of that body. Let us consider the elements a and b again, and suppose that a variable current is flowing through a and BO current through b ; then if we suppose that a variation in the intensity 108 KEi'oia — 1885. of a current is accompanied bj an alteration in the velocity of flow^ the acceleration of the positive electricity will, if we take Fechner's hypothesis, be equal and opposite to that of the negative ; but since there is a part of the force due to the moving electrified body which changes sign both with the electrification and the acceleration, the force due to the acceleration of the positive electricity will be equal in all respects to that due to the acceleration of the negative, so that there will be a resultant force on a unit of positive electtiuity at h, and this foi'ce is the electromotive intensity at b due to the alteration of the intensitj^ of the current in a. In this way we can explain the induction due to the varia- tion of the current in the primary circuit. Theories of this kind have been given by Gauss, Weber, Riemanu, and Clausius, and these writers have given expressions for the force between two electrified particles moving in any way. We shall after- wards consider these expressions in detail, but we may remark in passing that the theories of Gauss, Weber, and Riemann have much in common ; among other things they all lead to impossible results. In addition Clausius has shown that, unless we make Fechner's hypothesis about a current, viz. that it consists of equal quantities of positive and negative electricity moving with equal speeds in opposite directions, a current would on these theories exert a force on an electrified body at rest. The question of the forces due to moving electrified bodies is interesting in connection with electrolysis. Taking the ordinary view that the current is carried by the ions, we know from Hittorf 's researches that the anion and the cation move at different rates, so that the forces produced by these will be different ; hence we should expect an electrolyte conveying a current to exert a force on a charged particle at rest. We shall now go on to consider the various theories separately. Gauss's Theory.^ Gauss assumes that the force between two particles separated by a distance r and charged with quantities of electricity e and e' is along the line joining the particles and equal to where ii is the relative velocity of the two particles and c is a constant. This law will, if we make Fechner's hypothesis, explain the mecbanical force between two circuits ; but, since it contains no term depending on the acceleration, it cannot explain the E.M.F. produced by the variation of the strength of the current in the primary ; it is also inconsistent with the principle of the Conservation of Energy, and so we need not consider it any further. W. E. Weler's Theory.^ Weber assumes that the force between two charged particles, usiug the same notation as before, is ee r ^{^-M'S-K;:fr)} ' Gauss's theory was published after his death in his collected works, Gottingen edition, vol. v. p. 616. See also Maxwell's Electriclfi/ uivl Maijncthiit, 2ud edit, vol, ii. p. 440. - Weber's theory was published in 1846 in Abhundluwjeii der Kdmglich-Sdch-^ ON ELECTRICAL THEORIES, 109 This fonnnla is not inconsistent witli the principle of tlie Consei'vation of Energy ; making Fechner's hypothesis, it will explain the mechanical force between circnits conveying currents ; it will also exjilain induction due both to the motion of the primary and the alteration in the strength of the current in the primary. We shall see, however, that it makes a body under certain circumstances behave as if its mass were negative ; i.e. if it were acted on by a force in a direction opposite to that in which it is moving, its velocity would continually increase. Riemann'.s Theory. This is explained in his ' Schwere Electricitat uud Magnetismus,' edited by Hallendorff, p. 327. According to this theory the force be- tween two electrified bodies is not altogether along the line joining them, but consists of the following parts : — 1. A force along the line joining the particles equal with the same notation as before to ?'{i-'l} 2. A force on the first particle parallel to its velocity relative to the second equal to 2ee' dr oh^'^di- 3. A force on the first particle parallel to its acceleration relative to the second equal to -f, c'r where /is the relative acceleration of the particles. There are of course similar forces acting on the second particles, and we see from the form of the expressions of the forces that the force on the first particle is equal and opposite to the force on the second. Riemann's law of force is not inconsistent with the principle of the conservation of energy, and it explains the mechanical force between two circuits ; hence it must explain the induction of currents. We shall see, however, that it is open to the same objection as Weber's theory, viz. that it makes an electrified particle under certain circumstances behave as if its mass were negative. Glausius' Theory.^ If X, y, z are the co-ordinates of the first electrified particle, x' , y', z' those of the second, then according to this theory the x component of the force on the first particle is equal to — ee'x — < (J —vv cos i c^)~ > — -r -( - — 1 [dxX^ ' \l c^ dt\r dtj] With similar expressions for the components parallel to y and z, here jslschen Gesellscluift der WissenscMften, 18ifi, p. 211 ; it is reprinted in Electro- dynamische Maassbestimmnnijen, 1871. A good account of the theory is given in Maxwell's Electricity and Maynetimn, 2nd edit. vol. ii. chap, xxiii. ' This theory is given in Crelle, vol. 82, p. 85. There is also a fuU abstract in "Wiedemann's Beibldtter, vol. i. p. 143. to 110 BEPOET — 1885. V and v' are the velocities of the first and second particles respectively, and E is the angle between their directions of motion. We may analyse these forces a little differently, and say that the force on the first particle consists of — 1. A force along the line joining the pai'ticles equal to ee' f , , ; 1 -2- s J —vv cosejv- > 2. A force parallel to the velocity of the second particle and equal ec' <h- , 3. A force parallel to the acceleration of the second particle equal to ee' dv' ~'d^- 'df' We have, of course, corresponding expressions for the force on the second particle. Clausius' formulae differ from those of Gauss, Weber, and Riemann in two very important respects. 1. They mike the forces between two electrified bodies depend on the absolute velocities and accelerations of the bodies, while the others make them depend only on the relative velocities and accelerations. 2. They do not make the forces between the bodies equal and oppo- site, so that the momentum of the system does not remain constant. These results show that if this theory is ti'ue, we must take the ether surrounding the bodies into account. The first result can then be explained by supposing that the velocities which enter into the formulis- are the velocities of the bodies relatively to the ether at a considerable distance from the bodies, and the second result by supposing that the ether possesses a finite density, and that the momentum lost or gained by the bodies is added to or taken from the surrounding ether. The case is analogous to the case of two spheres A and B moving in an incompressible fluid ; in this case the forces on the sphere A depend on the velocities and accelerations of B relatively to the fluid at a great distance from the sphere, and ai-e independent of the velocity and accele- ration of A ; the forces are not equal and opposite, and the momentum lost or gained by the system is added to or taken from the momentum of the fluid. At the end of this section we shall see that, if we assume that variations in what Maxwell calls the electric displacement produce effects analogous to those produced by oi-dinary conduction currents, we get the same forces between moving electrified bodies as are given by Clausius' theory. Clausius' theory is not inconsistent with the principle of the con- servation of energy, and we shall see that it does not lead to the same diSiculty as the theoi'ies of Weber and Riemann, viz., that under special circumstances a body would behave as if its mass were negative. Assumino- that in an electric current we have equal quantities of positive and negative electricity moving with different velocities, Clausius has shown in the paper already cited that his theory gives Ampere's results for the mechanical force between two circuits, and the usual ON ELECTKICAL THEORIES. Ill expression for the induction due to tlie motion of the primary circuit, or variation in the strength of the current passing through it. Frohlich ' urges against Clausius' law that since, according to it, an electric current in motion exerts an electromotive force on a moving electrified particle, even though the particle is moving at the same rate as the circuit, every current on the earth's surface ought to exert an electromotive force on an electrified particle relatively at rest, since each is moving with the velocity of the earth. This force is one that can be derived from a potential, so that the integral of the force taken round a closed curve would vanish, and thus, even if this result were true, two circuits would not induce currents in each other if they were relatively at rest. Budde- points out, however, that the moving circuit would exert an electromotive force at each point of itself, and thus cause a separation of the electricity in the circuit, so that it would get coated with a distri- bution of electricity, the electrostatic action of which would balance that due to the action due to its motion on a point relatively at i^est. The velocities which enter into Clausius' formulje are velocities relative to the ether, so that if the ether moves with the earth, an electric current will, according even to this theory, exert no electromotive force on a point relatively at rest, and there will be no electrification on the surface of the circuit. The velocity c which occurs in all these theories is a velocity comparable with the velocity of light. General Considerations on these Theories.^ We shall now go on to discuss a general way of treating theories of the kind we have been considering. Perhaps the best way of doing this is to consider not the forces between the electrified bodies, but the energy possessed by them. If the energy depends on the electrification there will be forces between two electrified bodies. Now the potential energy depends on the electrification, and this dependence produces the ordinary electrostatic forces between two electrified bodies at rest. If, however, the kinetic energy as well as the potential depends on tlie electrification, then the forces between two electrified bodies in motion will be different from the forces between the same bodies at rest. An easy way of seeing this is by means of Lagrange's equations. If T be the kinetic energy, and x a co-ordinate of any kind, then we have, by Lagrange's equations, — — — = external force of type x. dt dx dx Hence if we have any term T' in the expression for the kinetic energy,, ■we may, if we like, regard it as producing a force equal to _ ^J^' + ^ dt dx dx A simple illustration of this is afforded by the centrifugal force. In » Frohlich, Wied. Ann., ix. p. 277, 1880. * Wied. Ann., s. p. 553, 1880. ' See Clausius ' On the Employment of the Electrodj-namic Potential for the Deterrnination of the Ponderomotive and Electromotive Forces,' I'kil. Mag., 1880, v. 10, p. 255. 112 REPORT— 1885. the expression for the kinetic energy of a moving particle there is the term ■where r is tHe distance of the pai'ticle ivo'.n some fixed point, and d the angle which the i^adius from this point to the particle makes with some fixed line ; m is the mass of the particle. This terra, by the above rale, will give rise to a force of type r, i.e., along the radius vector equal to and this is the ordinary centrifugal force. Now let us consider a moving electrified body. If it is symmetrical, ■and moves in an isotropic dielectric, it is evident that the electrification, if it enters at all, can only enter as a factor of the total velocity y, and cannot affect the separate components of the velocity differently. Let us suppose that the body is charged with a quantity of electricity denoted by e, then the kinetic energy, if it depends on the electrification, .must be of the form •where /(e) denotes some function of e. Now /(e) must be always positive, for if it were negative we could make \m + f{e) negative, and then the electrified body would behave like one of negative mass. The simplest form satisfying this condition which we can take for /■(e) IS ae^, where fi is some positive constant ; so that the form of ex- pression for the kinetic energy may be taken as Now let us go on to the case where we have two electrified bodies present, with charges e and e' of electricity ; let m and m' be their masses, q, q' their velocities, of which the components parallel to the axes of x, y, z nre (n, v, w)' ("'' ''^' ■> '^') respectively, the co-ordinates of the particles being (.r, ?/, z), (a;'_, 7/, s')- . If everything is symmetrical, the expression for the kinetic energy, if it only involves second powers of the charges of electricity, will be of the form \m(^ + \mcp + cie-^^ + /5e'^ ^'^-f-ee' k ./ {u, v, iv, «', v', w'} where/ (it, v, xv, n', v', iv') is a quadratic function 0? u, v, lu, u', v', w'. By Lagrange's equations we see that the last term will give rise to a force parallel to the axis of .r on the particle whose charge is e equal to I. dx dt du J with similar expressions for the forces parallel to ij and z. We can see, by substituting in this expression, that we get Weber's law if we make / = - < (lo — u') + 2 ^ [v — v') + (to ~ w') \ ; r I r r r J ON ELKCTRICAL THEORIES. 113 Riemann's law, if we make /= I {(u - ti'y + (v- v'y + (w - w'y] ; Clansins' law, if we make f-=~ {mm' + vv' + ww'\ ; and that we cannot get Gauss's law in this way ; this is in accordance with the fact that Gauss's law does not satisfy the principle of the conservation of energy. This way of considering the theories enables us to see that neither Weber's nor Riemann's formulae can be right, for if they were, an electrified body, when in presence of another, would, under certain circumstances, behave as if its mass were negative. Thus take Weber's law as an example : let us suppose that two electrified bodies are moving along the line joining them, which we may take as the axis of x ; then the expression for the kinetic energy, putting in the value of / which corresponds to Weber's law, is so that if im + ae2 + ^ r be negative, then the coefficient of if- in the kinetic energy will be nega- tive, and the body will behave as if its mass were negative ; and, by sufficiently increasing e' or diminishing r, we can make this expression negative, so that Weber's law leads to results which are inconsistent with experience. This result of Weber's law was first pointed out by Helmholtz. ' Exactly the same objection applies to Riemann's theory, and indeed we see that it will apply to any theory which makes the force between two electrified bodies depend on relative velocities and accelerations. The same objection need not apply to Claasius' theory, for substitut- ing the value of/ belonging to his theory, the kinetic energy equals {\m + ae2)22+ (i„i' + /3e'2)2'2 + ^^^, qq' cos e r so that the kinetic energy will be always positive if ilm + ae') (hn' + l3e'^)>ff£l^. This condition will evidently be satisfied if and this relation does not involve the electrification. We cannot assume that we can make r so small that this condition is not satisfied, for r has a minimum value depiending upon the shape and size of the electrified bodies. For example, if these are spheres, r cannot be less than the sum of their radii. On the other hand, a and /3 may be functions of the ' Ueber die Tlworie der EleUrodynamik. Crelle, vol. Ixxv. p. 635 • Collected Works. Bd. I, S. 647. 1885. 114 BEPOET — 1885. sizes of tte electrified bodies, and the geometrical relations may be such. that the condition written above must be always satisfied. Fliysical reasons why the force between two electrified bodies should depend on their velocities and accelerations. If we assume Maxwell's hypothesis that a change in the electric polarisation produces the same effect as an electric current, then we see that the kinetic energy of an electrified body must be different from the kinetic energy of the same body moving at the same rate but not electri- fied. For let us suppose that we have an electrified body at rest, and consider the amount of work necessary to start it with a velocity q^. It is evident that it will be greater than when it is not electrified, for when it is electrified and in motion the electric polarisation in the surrounding dielectric will be in changing, and so in addition to starting the body with a velocity q we have, if Maxwell's hypothesis be true, to establish what is equivalent to a field full of electric currents. The production of these currents of course requires work, so that more work is required to start the body with a velocity q when it is electrified than when it is not ; in other words, the kinetic energy of a moving electrified body is greater than that of one not electrified, but under similar conditions as to mass and velocity. In fact in this case electricity behaves as if it possessed inertia. In a paper published in the ' Philosophical Magazine,' April 1881, I have shown that the kinetic energy of a charged sphere of radius a and mass m moving at a velocity q where /z is the magnetic permeability of the surrounding dielectric and e the charge on the sphere. If there are two spheres in the field, then I have shown in the same paper that the kinetic energy — 2^2 +TT ~r 2 + 2'" 1 + T5 — T 2 + 3~^ 22 COS f, a a sst where corresponding quantities for the two spheres are denoted by plain and accented letters. We see from this expression that the forces between the spheres are exactly the same as those given by Clausius' formulae. It would not, however, be legitimate to go and develope the laws of electrodynamics from this result in the way that Clausius does, as Clausius' conception of an electric current does not accord with that of the displacement theory. We may remark that in this case the part of the kinetic energy due to the electrification is always positive. On theories which are based on dynamical considerations, hut which neglect the action of the dielectric. F, E. Neumann ' was the first to develope a theory founded on the principles of the Conservation of Energy. His theory was based upon the assumption that two elements of circuit ds, Js', traversed by currents I, i' possess an amount of energy equal to a^ijLss^ dsds', r ' ' Die mathematischen Gesetze der inducirten electrischen Strome,' Schriften der Berliner Academie der Wissemch., 1845. ON ELECrBICAL THEOBIES. 115 where A is a constant which depends upon the unit of current, r is the distance between the elements, and e the angle between their directions. F. E. Neumann showed that this assumption leads to the same law of force between two closed circuits as that given by Ampere, and also ex- plained by means of it the induction of electric currents, v. Helmholtz ^ has investigated the most general expression for the energy possessed by two elements of current which is consistent with the condition that the force between two closed circuits should be the same as that given by Ampere's theory. We shall consider this theory in detail, as it includes all theories of this class, and we shall wish to refer to it when we come to discuss the relative merits of the various theories, v. Helmholtz hegins by showing that the most general expression for the energy of two elements of circuit consistent with Ampere's laws for closed circuits is 1 A^L^ 1(1 ^ ^) (508 £ + {1-1) cos e cos &} ds ds', where 9 and 6' are respectively the angles ds and ds' make with the line joining the elements, ^ is a constant, and the other symbols have the same meaning as before. Let us call this quantity T ; then we know thatT denotes the existence •of a force dT/dr or - i ^—^ {(1 + ^) cos £ + (1 - h) cos d cos 8'} ds ds' along r, and a force — dT/rdd at right angles to r in the plane of ds and r, and in such a direction that it tends to diminish d ; this force equals i -^Ll^^l-k) fsin fl cos 6' + cos sin d' —^ ; rand since dd' ' ^=cos ,, where rj is the angle between the plane containing r and ds and that containing r and ds', the transverse force A^ I i' = ^ 2 — 0-~^) W'^ " COS 0' + cos 9 sin 6' cos r)] . We see that these'forces will coincide with those assumed in Korte- weg's theory if the quantities a, I, c, d, which occur in that theory, have the following values : o= — A' b= -1(1 + ^^ A» d=^(l-k)A^. So that whatever ^be the value of /,-, these quantities", satisfy the con- •dition 2a + b + c-2d= - .3A2. ' Crelle, Ixxii, p. 57; Gesammeltc Werke, vol. i. p. 645. IS 116 REPORT — 1885. According to Stefan, it is necessary if two circuits have a potential that 2a+b-¥ c-2d=0. But Stefan did not consider the couple exerted by one element of circuit on another. The couples acting on the element els' will be as follows. There will be a couple tending to increase 6', i.e. a couple- whose axis is at right angles to both ds' and r, equal to dT/dd', i.e. to 1 4li-L {(1 + Jc) sin cos & cos »,-2 cos 9 sin d'}, and another couple tending to increase v, i.e. a couple whose axis is along the line joining the elements equal to dT jdr), i.e. to 1 A^ 2 (l + Z;) sin 6 sin 0' sin >;■ r "We see that these will agree with the couples in Korteweg's theory of r ' r r Let us return to the consideration of the energy of the circuits, and suppose that, instead of currents flowing along linear circuits, we have a distribution of them throughout space. If n, v, w be the currents in the element dx, dy, dz, then the part of the energy contributed by this element will be - A2 {[]u+Yv+Ww}'dx dy dz, where d^ dr) d^, with symmetrical expressions for V and W, where r^ = (x - ly + (1/ - vT- + (z - zy. We may write the expressions for TJ, V, W in the form v=i(i-A-)-^ + jj|^d^d,dc where4'= III {-% + - | + ^'^ |) ^'' ^"^ "^^ ■ If u, V, IV are the components of the ordinary conduction current, e the volume density of the free electricity, then du dv dw de \ dx dy dz dt' and if 1, m, n be the direction cosines of the normal to a surface at which ON ELECTKICAL THEOBIES. 117 the currents become discontinuous, a the surface density of the electricity on this surface, then I (u—u^) + m (v—v^) + n (lu—xu^) -f __ = 0. (XiJ/ Remembering these equations, 4/ may be transformed into \\\ r —-dx dy dz + \\ r — - ds : JJJ dt -^ ^ ]] dt ' ■or if (j> denote the electrostatic potential of the free electricity, we see \h ^ — ~ dx dy dz. ^ 27r JJJ r dt ^ Substituting this value of ^ we find dxdt ay at We also see that ^^W = (l-k)^-4.7riv. dzdt dx dy dz dt In order to get the equations connecting the electromotive force with the variation of the electrodynamic potential, Neumann made use of Lenz's law, and assumed that, since by that law the electromotive force tending to"'increase the current in an element of circuit moving with a velocity ■w in the direction s would be of the same sign as — Xzy, where X is the force along s on the element per unit of length per unit of current flowing through it, it was actually equal to this quantity multiplied by a constant c, i.e. to — cKw; but if Ti ds be the energy of the element of current whose length is d&, and current strength i, X=^'^ and w=^ -=- ; dt so that the electromotive force per unit of length of the element __ ^ ds ds dt _ (IT -~'dT 118 REPORT— 1885. V. Helmholtz has shown that it follows from the principle of the Conser- vation of Energy that if the energy in the elements dx, dy, dz, traversed by currents u, v, w, be A2 (TJu+Yv + Ww) dxdydz, then the components of the electromotive force parallel to the axes x, y, z respectively, due to the variation in the electrodynamic potential, will be -A^^, -A2'!Y, -A^^-^; dt ' dt ' dt the free electricity produces an electromotive force whose components are d<f) d<j> d<ji daj' dy' dz' so that the total electromotive force parallel to x, y, z dx dt Now if a be the specific resistance of the conductor, mi equals the elec- tromotive force parallel to the axis of .v, so that dx dt so that by the preceding equations 47rl ^ \lxdtl dx dt* with similar equations for V, W. The quantities U, V, W and their first difierential coefBcients with respect to x, y, z are continuous, and these equations enable us to find them if we know the value of ^,. the potential of the free electricity. Helmholtz shows that the whole- energy in the field due to the currents may be written so that if h be negative, this expression may become negative, and in' that case the equilibrium would be unstable ; hence we conclude that only those theories are tenable for which /.■ is positive. The equations written above are those which hold in a conductor,, in an insulator the equations are r2 ■ ^=(i-"> Wit dz dt v. Helmholtz shows that in the conductor the electrostatic potential <^ 1 satisfies the equation ON ELECTRICAL THEORIES. 119 SO that if tlie conductor has an infinitely small resistance, the equation becomes v-»2 A — A 2?. V^(t> = A.Vc'^ This represents a wave motion, the velocity of propagation of which is l|A^yk. If 1c, as in ISTeumann's theory, be equal to unity, then the velocity of propagation is 1 /A, and from the value of A, found from experiments on the force between circuits conveying currents, this is nearly equal to the velocity of propagation of light. Thus, according to Neumann's theory, in a perfect conductor an electrostatic disturbance is propagated with the velocity of light. In an insulator satisfies the equation and this represents a motion propagated with an infinite velocity, and thus, according to this theory, an electrostatic disturbance is propagated with an infinite velocity in a perfect non-conductor. In an imperfectly conducting substance the velocity of propagation of a wave motion would depend upon the length of the wave. Let us now go on to consider, what, according to this theory, are the forces acting on an element of circuit conveying a current. Let us suppose that the element ds forms an element of a circuit through which a current t is flowing ; then the energy of the circuit will be J I as as ds J In order to find the force parallel to x, let us suppose that each element of the circuit receives an arbitrary displacement x, parallel to the axis of X ; then the alteration in the energy will be ^,r f'i^'^+'^du^dWdzi^^^^^^.r^,^^^^ ■ J L dx ds ax US x as J } ds Integrating the second term by parts, we see that it may be written TA^ TJ^a;1 — A^ f t / ^U (?a; rfU */ c^ W cZs "1 , ] \ dx ds dy ds dz ds J ' Substituting this value for the second term, we see that the alteration in the energy, = C-'-»3 + -f • { I (^J-f ) -S (f - f ) } - * ^ hence we see by the Conservation of Energy that there is a force on each element of current parallel to the axis of <c, equal to ^ / dy /dV _dV\ _dz fdJJ _dW\ T . j l ds\dx dy J ds\dz dx J J ' and by symmetry forces parallel to y and z equal respectively to Jdz/'dW_dY\ dxfdY dV\ 1 ^2. Ldsvd;/ dz J ds\dx dyj j J^fd^_dW\_clyfdW_dV\l.^ \ ds\dz dx J ds\ dy dz) J 120 EEPORT — 1885. so that the resultant of these forces is at right angles to the element. In addition to these forces there are other forces at places where the quantity lU is discontinuous, or, since U is continuous, at places where i is discon- tinuous, whose components parallel to the axes of x, y, z, are respectively A2[J?(, A2V^\, A^W^i; bnt II equals de/dt, the rate at which the free electricity is increasing at the place, so that we have at any place where the free electricity is changing a force whose components are dt A2V dt' A^W^^ dt We saw before that the force acting on the circuit per unit length is at right angles at each point to the element of circuit at that point, so that, unless a circuit includes places at which the quantity of free electri- city is changing, the circuit will behave as if it were acted on by forces which were everywhere normal to the elements on which they act. In the experiments which have been made to test whether the force on the element is at right angles to it, there have been no points where the free electricity is changing, so that these experiments do not contradict Neu- mann's theory, although, according to it, the force on an isolated element is not necessarily at right angles to that element, for in addition to the forces normal to the element we have forces equal to A^UcZe jdt, A?Yde j dt, A^W de/dt parallel to x, y, z respectively, acting at the ends, the resultant of these two forces is a force whose components parallel to the axes of x, y, z are respectively A^dedUds dt ds A^dedVds dt ds A^dedWds dt ds and as these forces are not necessarily at right angles to the element, the resultant force is not necessarily so ; the eifect of these forces could not, however, be detected unless there was a discontinuity in the current. V. Helmholtz in the memoir ' which we have already quoted shows that, according to his extension of F. E. Neumann's theory, the forces between two elements of circuit ds and ds' may be looked upon as made up of — (1) A i-epulsive force on ds due to an end of ds', equal (per unit length) to . , de'l dr atrds " Ueber die Theorie der EJelitrodynaviih, dritte Abhandlung, Crelle, Ixxviii. pp. 273, 324, 1874; Gesammelte Werke,^. 723. ON ELECTRICAL THEORIES. 121 (2) A repulsive force on ds due to ds', equal per unit length to ^ < 2 cos (tZif ds') — 3 cos {r ds) cos (r ds') > ; (3) A repulsion between the ends of ds and ds', equal to - ^(1 + *) ^' If ^ (4) A repulsion on ds', due to an end of ds equal per unit length to — A^t'^-^. dt r ds The second of these is the only one considered in Ampere's theory. We must remember in calculating these forces that each element has two ends. Let us now go on to find the couples acting at each point of the circuit. If the tangent to the circuit makes an angle with the axis of z, and the plane containing the tangent and the axis of z an angle f with the plane of xz, then we may write -^ = sin cos 0, ds -^ = sin 6 sin d>, as ' dz a -— = cos 0, ds so that with the same notation as before the energy equals A^f. ru^+v$ + wtV> J V 'Is ds dsj = A^ £ (U sin e cos ^ + V sin sin (/) + W cos 0) ds, so that if ^ increase by c^, the alteration in the energy equals A^ I I ( — U sin 9 sin ^ + V sin cos ^) h<p ds, so that the couple tending to increase (j>, i.e. the couple whose axis is parallel to the axis of z, equals A^ I (V sin d cos <^ — U sin sin <^) per unit length of current ; this may be written A^ ("vt - U^V \ ds dsJ hence the couples parallel to the axes of y and x are by symmetry re- spectively I ds ds J ' A^i Iw'^-V^\. I ds ds J 122 REPOET — 1885. Tlae axis of the resultant couple is perpendicular to the element and to the vector whose components are U, V, W. In another paper • v. Helmholtz discusses the force acting per unit of volume on a conductor traversed by electric currents ; he shows that, according to the potential theory, if u, v, w are the components of current through an element clx cly dz, and X, Y, Z the components of the force acting on this element of volume per unit of volume, then V A,r C^^ ^U\ AiW cZU\ ^del ^=^'bU-dy) + ^[^.-d-J + ^dij ^ . r fdXJ dV\ /dW dy\ „ del rr . , r /"'^U c?W\ (dY dW\ ^ del He then discusses the application of the potential law to sliding contacts, that is, contacts such as those made by a wire dipping into mercury ; in the derivation of the forces from the potential law it is assumed that the displacements are continuous, and it might be objected that we have no right to apply the law in this case as the motion of the wire and the mercury seems at first sight discontinuous, v. Helmholtz, however, points out that, as the wire carries the mercury with it as it moves, the motion is not really discontinuous and that Neumann's law is applicable. The question of sliding contacts comes prominently forward when we compare the various theories ; we shall return to it again in this con- nection. V. Helmholtz also in this paper investigates the electromotive foi'ces acting on a conductor in motion ; he shows that if the components of the velocity of the conductor at any point are a, /3, y, then P, Q, R, the com- ponents of the electromotive force, are given by the equatioit „ - /dU dV\ /dXJ dW\ d ^^^ ^^ ^ ^ with similar equations for Q and R. He also investigates the difference between the results of Ampere's and Neumann's theory for the E.M.F. due to induction. The results are complicated ; for practical purposes it is sufficient to notice that when there is a mechanical force tending to make the body move in a certain direction, there must be an E.M.F. when the body moves in that direction. C. Neumann^s Theory. C. Neumann assumes that the electric potential energy is propagated with a finite velocity, and that if two electrified bodies are in motion, the mutual potential energy is not ee'/r, where r is the distance between them, but ee'/r', where r' is the distance between them at a time t before, where t is the time taken by the potential to travel from the one body to the other. The energy considered in C Neumann's theory is a kind of energy quite different from any that we have experience of; it is not poten- ' Ueher die Theorie der Elehtrodynamik, Crelle, Ixxviii. pp. 273-324, 1874 ; Gesammelte Werke, vol. ii. p. 703. ON ELECTRICAL THEORIES. 123 tial energy, because that at any time depends only on the position of the system at that time ; it is not kinetic, because that depends only on the position and velocity of the system at the time under consideration, ■whilst Neumann's energy depends on the velocity and position of the system at some previous time. In spite of ail this, however, Neumann applies the ordinary dynamical processes to this energy just as if it were kinetic or potential ; and in this way arrives at the same expression as- Weber for the force between two moving electrified bodies. The rest of the theory is the same as Weber's, except that Neumann's assumption about the nature of a current is different from Weber's. According to Weber, an electric current consists of equal quantities of positive and negative electricity, moving with equal velocities in opposite directions. According to Neumann, the positive electricity alone can move, the nega- tive being attached to the molecules of the conductor. Riecke and Clausius have shown that with this assumption and Weber's law a steady current must exert a force upon a particle at rest and charged with electricity, and must in consequence produce an irregular distribution of electricity over any conductor in its neighbourhood. Theories tohicli are founded on dynamical considerations and which take into account the action of the dielectric. In the theories we have hitherto considered, the influence of the medium which exists between the currents has been left altogether out of account. In the theories which we shall now proceed to discuss, the in- fluence of this medium is taken into consideration. This is, perhaps, the most important step that has ever been made in the theory of electricity, though from a practical point of view it is comparatively of little import- ance ; in fact, for practical purposes almost any one of the preceding theories will satisfy every requirement. Faraday was the first to look upon the dielectric as an important agent in electrical phenomena ; he was led to this by his desire to get rid, as far as possible, of the idea of action at a distance, which was so pre- valent in his time, but to which his researches have given the death-blow. In his ' Experimental Researches,' § 1164, speaking of electrostatic in- duction, he says, ' I was led to suspect that common induction itself was in all cases an action of contiguous particles, and that electrical action at a distance (i.e. ordinary inductive action) never occurred except through the influence of surrounding matter.' And later on he gives his- views as to the nature of the efiect in the medium; in § 1298 of the- ' Researches ' he says, ' Induction appears to consist in a certain, polarised state of the particles into which they are thrown by the electri- fied body sustaining the action, the particles assuming positive and negfitive points or parts, which are symmetrically arranged with respect to each other and the inducting surfaces or particles. This state must be a forced one, for it is originated and sustained only by force, and sinks to the normal or quiescent state when that force is removed. It can be continued only in insulators by the same portion of electricity, beca.use they only can retain this state of the particles.' He gives an ex- perimental illustration of his view in § 1350. He says, ' As an illustration of the condition of the polarised particles in a dielectric under induction I may describe an experiment. Put in a glass vessel some clear rectified 124 EEPOET— 1885. oil of turpentine, and introduce two wires passing tlirough glass tubes, when they coincide with the surface of the fluid and terminating in balls or points. Cut some very clean dry white silk into small particles, and put these also into the liquid ; then electrify one of the wii'es by an ordinary machine and discharge by the other. The silk will immediately gather from all parts of the liquid and form a band of particles reaching from wire to wire, and if touched by a glass rod will show considerable tenacity ; yet the moment the supply of electricity ceases the band will fall away and disappear by the dispersion of its parts. The conduction by the silk is in this case very small, and after the best examination I could give to the effects, the impression on my mind is that the adhesion of the whole is due to the polarity which each filament acquires, exactly as the particles of iron between the poles of a horse-shoe magnet are held together in one mass by a similar disposition of forces. The particles of Bilk therefore represent to me the condition of the molecules of the dielectric itself, which I assume to be polar, just as that of the silk is. In all cases of conductive discharge the contiguous polarised particles of the body are able to effect a neutrahsation of their forces with greater or less facility, as the silk does also in a very slight degree. Further we are not able to carry the parallel, except in imagination ; but if we could divide each particle of silk into two halves, and let each half travel until it met and united with the next half in an opposite state, it would then exert its carrying power (1307), and so far represent electrolytic discharge.' And it is not only in statical electricity that Faraday recognised the importance of the dielectric. When he is discussing his discovery of the induction of currents, which he ascribes to the assumption of what he called the electrotouic state by the body in which induced currents are developed, he says, § 73, ' It may even exist in non-conductors,' that is, that there is an electromotive force acting on the surrounding dielectric due to the variation in the primary current. Again, in § 1661, he says, * Now though we perceive the effects only in that portion of matter which, being in the neighbourhood, has conducting properties, yet hypotheti- cally it is probable that the non-conducting matter has also its relations to, and is affected by, the disturbing causes, though we have not yet dis- covered them. Again and again the relation of conductors and non- conductors has been shown to be one, not of opposition in kind, but only in degree (1334, 1603) ; and therefore for this, as well as for other reasons, it is probable that what will affect a conductor will affect an insulator also, producing, perhaps, what may deserve the term of the electrotonic state (60, 24"2, 1114).' And though he was unable to detect these effects experimentally, the following paragraph (1728) shows that his belief in their existence was not shaken : ' But then it may be asked. What is the relation of the projierties of insulating bodies, such as air, sulphur, or lac, when they intervene in the line of magnetic action ? The answer to this is at present merely conjectural. I have long thought there must be a particular condition of such bodies, coi'responding to the state which causes currents in metals and other conductors (26, 53, 191, 201, 213) ; and considering that the bodies are insulators, one could expect that state to be one of tension. I have, by rotating non-conduct- ing bodies near magnetic poles, and poles near them, and also by causing powerful electric currents to be suddenly formed and to cease around and about insulators in various directions, endeavoured to make some 1 I ON ELECTRICAL THEOraES. 125' sncli state sensible, but have not succeeded. Nevertheless as any such state must be of exceedingly low intensity, because of the feeble intensity of the currents which are used to induce it, it may well be that the state may exist, and may be discoverable by some more expert experimentalist, though I have not been able to make it sensible.' Maxwell was the first to express Faraday's ideas in mathematical language. In his papers on ' Physical Lines of Force ' in the ' Philoso- phical Magazine ' for March, April, May, 1861, and January, February, 1862, he developes a theory of electricity according to which the enero-y of the electro-magnetic field resides in the dielectric as well as in the con- ductors ; later, in the ' Philosophical Transactions ' for 1865, he greatly extended Faraday's ideas as well as put them into definite mathematical language, and this without reference to any special theory of the mechan- ism which produces electrical phenomena. We shall devote some time to discussing Maxwell's theory, as it is freer from serious objections than any other, while at the same time it covers a much wider ground. We shall begin by referring to Maxwell's view of the state of the dielectric in the electric field. Maxwell supposes that the dielectric i& changed, and perhaps the clearest way of describing this change is that of Faraday in the extract already quoted. Maxwell's nomenclature as to this change is a little unfortunate ; instead of speaking, like Faraday, of the polarisation of the dielectric, he speaks of the change as consistino- of an electric displacement, which in isotropic media is in the direction oi the electromotive force. Mathematically the two things are identical • we may either say of a wire that it is negatively electrified at one end a' and positively at the other end B, or else that there is a displacement of positive electricity from A to B, so that there is an excess of positive electricity at B and a deficiency at A. But though the words in a mathe- matical sense are identical, still the word displacement seems to connote special qualities which limit the generality of the conception in an unde- sirable way ; the word displacement seems to imply motion in the direction of displacement, while polarisation only implies that there is a vector change of some kind in the dielectric. The condition of the dielectric is quite analogous to the state of a piece of soft iron placed in a magnetic field. The polarisation or displacement is in isotropic media in the direc- tion of the_ electromotive force and proportional to it, just as the magnetic induction in isotropic media is in the direction of the mao'netic force and proportional to it. It was this proportionality combined with the fact that as soon as the electromotive force is removed the dielectric sprino-s back, as it were, to its original state, that led Maxwell to use the word dis- placement. He looked on the case as analogous to that of an elastic solid, which springs back to its original position when the external force is removed, and in which the displacement is proportional to the im- pressed force. To avoid any unnecessary definiteness we shall use the term dielectric polarisation instead of electric displacement. Thus according to this view the dielectric in the electric field is polarised. This polarisation means change of structure of some kind, and to produce this change of structure work is required. The energy in the polarised dielectric will be greater than the energy when it was unpolarised, for if the energy were less the dielectric would go into the polarised condition of itself, without the application of any external forces. It is rather difficult to see what is meant in Maxwell's theory by the- phrase ' quantity of electricity.' According to the old two-fluid theory 126 BEPORT — 1885. an electrified body was supposed to contain a certain quantity of some- -thing called electricity, rules were pven for measuring this quantity, and the phrase ' quantity of electricity ' meant something quite definite. In Maxwell's theory, where everything is referred to the dielectric, the meaning of the phrase is not so obvious. We can, however, arrive at some idea of what is meant by the consideration of what are called ' tubes of force.' Let us suppose at first that the dielectric is air. A line of force is a line whose direction at any point coincides with the direction of the electromotive force at that point, so that we may conceive the electric •field to be filled with lines of force. If we consider the lines of force passing through some small closed curve, they will form a tube, and such a tube is called a tube of force ; and if the dimensions of the tube are such that the product of the cross section at any point and the electromotive force at that point is constant and equal to iir, the tube is called a unit -tube. We may thus conceive space to be filled with unit tubes of force. Since the electromotive force inside a conductor vanishes these tubes will end at the surface of a conductor. And the quantity of electricity on the conductor will be equal to the excess of the number of lines of force which leave the conductor over those which enter it. A tube is said to leave the conductor when the direction of the electromotive force is along the normal vdrawn outwards, and to enter it when the direction of the electromotive force is along the normal drawn inwards. As the conductor moves about it may be supposed to carry the tubes of force along with it, so that the number of tubes which end on the conductor remains constant. This way of look- ino- at electrification is quite satisfactory as long as we keep to one dielectric air ; when we have to consider difi'erent dielectrics it requires modification, because the electromotive force changes abruptly as we pass from one dielectric into another, so that a tube which was a unit tube in -one dielectric is not so in another. It is easy, however, to extend the definition of unit tubes so as to meet this difficulty ; for if the tubes pass from one dielectric A into another B the ratio of the product of the cross ■section and electromotive force is constant for all the tubes and depends only on the nature of the dielectrics ; this ratio is the ratio of the specific inductive capacities in B and A. Air is taken as the standard dielectric, and the specific inductive capacity of another dielectric A is the ratio of the product of the electromotive force and cross section of a tube in air to the product of the same quantities for the same tube in the dielectric A. Thus if we amend our definition and say that a circuit tube is one such that the product of the cross section, the electromotive force, and the specific inductive capacity of the medium in which the cross section is situated is equal to 4?r, then the quantity of electricity on a conductor is equal to the excess of the number of unit tubes which leave the conductor over the number of those which enter it. In this way we get an idea of Vi^hat is meant by ' quantity of electricity ' in Maxwell's theory. Maxwell accounts for the forces observed between electrified bodies by a system of stresses in the dielectric separating them ; as, however, at present we wish to compare Maxwell's theory with other theories which do not touch upon this point, we shall discuss this part of the theory separately later on and go on to discuss those points which are involved in all the theories. The next great point in Maxwell's theory is the development of Faraday's remark that the electrotonic state may exist even in non-con- •ductors, i.e., that the dielectric surrounding a changing current is acted I I ON ELECTRICAL THEOEIES. 127 •on by electromotive forces which polarise it. This statement is one as to whose truth nobody seems to entertain any doubt, whilst the state- ment that changes in the dielectric polarisation produce effects analogous to those produced by ordinary conduction currents is by no means so universally received, and yet the one seems the necessary consequence of the other. If we regard the whole electric field as a dynamical system, and to fix our ideas consider an element a of the dielectric, and the cur- rent, which is supposed to vary, then, since a variation in the current polarises a, i.e., produces a change in its structure, there must be mechanism connecting the current with the element a ; but if this is so then it follows from dynamical principles that a non-uniform variation in the structure of rt must produce a change in the current — in other words, that a change in the rate of change of the polarisation of a pro- duces an electromotive force on the current, i.e. that the change of polarisa- tion produces an effect analogous to that of an ordinary conduction current. We may illustrate this by a purely dynamical example. Sup- pose we have a dynamical system defined by two co-ordinates p and q, and let T be the kinetic energy of the system and V the potential energy ; then by Lagrange's equation the force tending to increase q = - ^+ cZT__cZ^ dT dq dq dt dq' Now if there is a force tending to alter q which depends upon the acceleration of p, there must be a term in the kinetic energy of the form but if we apply Lagrange's equations to the p co-ordinates we see that •this term implies the existence of a force tending to increase p equal to -lit ^^' so that an acceleration of q will produce a force tending to alter p. To make this applicable to the case of the current and the dielectric, we have only to suppose that p represents the current, q the polarisation of the dielectric. That a change in p produces a change in q is shown by the fact that the dielectric is polarised when the current is changing, and this shows that there must be a term of the form A.pq, in expression for the kinetic energy ; from this it follows that a change in q, i.e., in the rate of change of the polarisation, will produce an E.M.F. on the circuit. As the variation of the dielectric polarisation produces the same effect as a conduction current, we must in the case, when both conduction current and alteration in the polarisation are present, look upon the true or effec- tive current as the sum of the conduction current and the change in the polarisation. The components/, g, h of the dielectric polarisation are defined by the equation /=^x 9=~Tr h=^Z, 4n- 47r 4n- where K is the specific inductive capacity of the medium, X, Y, Z the components of the electromotive force. If u, v, w are the components of the effective current, p, q, r the components of the conduction 128 KEPOET — 1885. current, then Maxwell in his paper on a ' Dynamical Theory of the Electromagnetic Field,' ' Phil . Trans., 1885,' puts Since ^ + 1^ + ':^r = _ ^ dx dy dz dt , df . da dh and -jL + ^ + -r-= P^ ax ay dz ■where p is the volume density of the free electricity, we see that du dv div p. dx dy dz If the values of the quantities in a medium A be denoting by putting the suffix 1 to the symbols representing them, and those in another dielectric B by putting the suffix 2, then if I, m, n are the direction cosines of the normal from A to B, we have at the boundary of the two media ^ (ih-p-i) + m (qi-q^) + n (ri-ra) = ^ ^ (/i -/2) + ''* (ui -Oi) + '^ {K-1h) = -<^, where (r is the surface density of the electi'icity ; thus I (ui—u^) + 111 (V1—V2) + n (W1 — W2) =0; so that u, V, iv satisfy the same equations as the components of the velocity of an incompressible fluid. This assumption about the magnitude of the effects produced by the alteration in the dielectric polarisation makes the mathematics of the theory as simple as possible. If Maxwell had merely assumed that the alteration of the dielectric polarisation produces effects analogous to those produced by ordinary conduction currents, and that the equivalent con- duction current was proportional to the rate of alteration of the dielectric polarisation, then these equations would have been , dY "=^+"^' ^ dZ so that in a homogeneous dielectric du dv dw '''^ / 1 _ 4 """ "l d^ ckf ih dt\ TJ' Z(w,— 1*2) + m. {v^—v^) + n {w^—Wi) = y+a^ dT , dN, dlif It ' dt ^ dt where N is the component of the electromotive force normal to the surface . ON ELECTRICAL THEOEIES. 129 Maxwell's assumption is that a=K/47r, and this makes the equations much simpler ; it is, however, important to remember that Maxwell's theory of the dielectric involves the two assumptions— 1st. That alterations in the dielectric polarisation produce effects analogous to those of ordinary conduction currents ; 2nd. That the magnitude of the equivalent conducting current = d I -— F V Idt, where F is the electromotive force at the point ; this is equivalent to saying that all the currents are closed currents, and that there is no discontinuity in them. Maxwell developes his theory by means of the principle of the Con- servation of Energy. Let us consider an electric field full of currents, whether ordinary conduction currents or polarisation ones. Then this field may be looked upon as a material system, and all the phenomena have to be explained as the effects of the motion of this system ; a current must be looked upon as a change in the structure of the system, and so capable of representa- tion by means of the differential coefficients of the co-ordinates fixing the system ; we can thus represent the current at each point as the differential coefficient of some generalised co-onlinate fixing the system ; the components u, v, w of the current passing through an element dx, dy, dz may be looked upon as the rates of change of some generalised co-ordinates ; we may write the energy as if 1 1 (Fm + Gv + B.w}dx dy dz, where F, G, H may be looked upon as momenta corresponding to u, V, w. It remains to identify F, G, H with known quantities. Maxwell does this by the aid of Faraday's result, that the electromotive force round a circuit equals the rate of diminution of the number of lines of force passing through it. Let us consider a single linear circuit in which the current is i, or say dqjdt, then the energy = ^J^h^- + G^+-B^\ds, J at L ds ds ds J where ds is an element of circuit ; but by Lagrange's equation the force tending to increase q, i.e., the electromotive force in the circuit, = -^{(F'^^+GiM+K^')ds; dtj\ as ds ds) so that ffF ^4- G'i^+H^V* ]\ ds ds ds) equals the number of lines of force passing through the circuit ; but if d^ be an element of surface closing up the circuit, I, m, n the direction cosines of the normal, then by Stokes' theorem f( F — + G^ + R—^ds ds ds dsj 1885. ll{'{^-f)+-(f-f)-'(rf)}-^ E. 130 EEPOET — 1885. but the number of lines of force passing through the circtiit = I (JO' + ini + nc)dS, ■where a, h, c are the components of magnetic induction, so that dy dz ' dz dx ^^dG_clF dx dy To connect a, h, c with the current, Maxwell makes use of the prin- ciple that the line integral of the magnetic force taken round any closed curve equals the current flowing through the curve. This leads to the equations — . dy dl3 4;r«=— — — , ay dz . da dy dz ax A dft da dx dy so that if /u be the coefficient of magnetic permeability, . dc db dy dz and so on. Substituting the values of a, b, c, given above, we find dx I dx dy dz i with similar equations for G and H. Now V. Helmholtz, in his paper ' Ueber die Bewegnngsgleichungen der Elektricitat fiir ruhende leitende Korper ' (Crelle, Ixxii. p. 57 ; Gesam- melte Werke, ii. p. 545), has investigated the most general expressions for F, Gr, H, consistent with the force between two closed circuits agree- ing with that indicated by Ampere's theory, and he finds that if the circuits are closed circuits, as Maxwell assumes all circuits to be, then dx dy dz and therefore 477^^= — v ^F, with similar equations for G and H. These equations are sufficient to determine the quantities F, G, H. Maxwell does not at once put dFldx + dG/dy + dH.ldz=0; he writes for this quantity, and puts X= \—dx dy dz. Then F=JJ|^da; dy dz+-^; ON ELECTRICAL THEORIES. 131 as, however, he subsequently puts J=0, we may at once simplify the equation by making this assumption. Since the kinetic energy equals 1 ( [ [ (Fu + Gv + mu) dx dij dz, we see by Lagrange's equations that the electromotive force tending to increase u dt ' in addition to this there is the force arising from the electrostatic poten- tial (j), so that the total electromotive force parallel to the axis of x ^_dF_d<j> dt dx so that if (s be the specific resistance of the substance, K its specific induc- tive capacity, then 47r . dF d(^ ''P=K^=-dt-Tx' '^ '"' ^'^dt Adt dxi 4:7r\dt^ dicdti ' tut we saw before that 47r/i!{= — V ^F ; substituting for u this value, we see ^^F^^fdY d^l Jd^ d^^ <r I dt ^dx / ^"^^ 1 dt^ ^dx dtr ^ihus in the dielectric the equation becomes ^idt^^dxdtr in the conductor o- \ dt dx i The equation for the dielectric shows that it represents a wave-motion propagated with the velocity 1/v/K^; the numerical value of this velocity agrees very approximately witla the velocity of light, and this led Max- well to the theory that the changes in the structure of the dielectric which take place when the dielectric is polarised are of the same nature as those which constitute light. This theory, which is called the electro- magnetic theory of light, might almost as justly be called the mechanical theory of dielectric polarisation. Earchhoff, in his paper ' Ueber die Bewegung der Blectricitat in Drahten ' (Pogg. Ann., vol. c. 1857 j -Gesammelte Werke, p. 131), was the first to point out that some elec- trical actions are propagated with the velocity of light. In this paper he considers the motion of electricity in wires whose diameters are small compared with their length. There are three things which have to be con- sidered in this problem — (1) the self-induction of the electric current, and k2 132 REPORT— 1885. if the medium be taken into account, that of the polarisation currents in the dielectric. This self-induction produces very much the same effect as if the electric current possessed momentum— (2) the electrostatic action of the free electricity which tends to bring things to a definite state, and corresponds very much to the spring in a material system. Then, lastly, there is the electrical resistance, which corresponds to fi'iction in an ordinary system. We see from the analogy that if the resistance be small enough, the electrical system will vibrate ; if, however, the resistance is large, the electrical disturbance will be propagated in the same way as heat. Kirchhoff in his paper considers the propagation of electrical disturbance along a wire under various conditions : we shall only consider here one of these cases ; that of an endless wire. In his solution Kirchhoff only considers the self-induction of the current flowing along the wire ; he does not consider the effects in the surrounding dielectric. He shows that if e be the quantity of electricity per unit length of the wire, and e=X sin ns, where s is the length of a portion of the wire measured from some fixed point, then X satisfies the differential equation cPX c^r dX c2 d''X dt^ I6yl dt 2 ds^ ' where c is a quantity which occurs in Weber's theory, and is the velocity with which two charged particles must move if the electrodynamic attraction between them balances the electrostatic repulsion ; r is the resistance of the wire in electrostatic measure ; y = log If a, where I is the length of the wire and a the radius of its cross section. The form of the solution of this equation depends on the magnitude of If this quantity be large, the solution takes the form representing the- propagation of a wave along the wire with the velocity c/\/2. Weber's researches show that this velocity is very nearly equal to the velocity of light. If, however, the above-mentioned quantity be small, then the solution of the equation takes the same form as the formula which expresses the conduction of heat along the wire. We must not, however, take this to mean that the electric disturbance is propagated with an infinite velocity, so that if we had an infinitely delicate electrometer at a finite distance from the source of disturbance we could detect an electrifi- cation after an indefinitely short time, for it seems obvious that the electrical resistance cannot increase the velocity of propagation any more than the resistance of the air could increase the velocity of propagation of a disturbance along a line of particles connected by an elastic string. The conditions at the end help to determine the form of the solution, and these cannot make themselves felt until the disturbance has reached it ;. thus the heat form of solution probably only holds after a time from the commencement of the disturbance greater than the time taken by light to travel along the wire. If we take the case of a copper wire one square centimetre in area, we shall find that the wave form of solution will hold if the wire is not more than 100 miles in length, while the heat form will correspond to wires which are much longer than this. Kirchhoff's ON ELECTRICAL THEORIES. 133 solution only refers to the propagation of a disturbance in a conductor, while Maxwell's refers to the propagation of such a disturbance in the dielectric. Maxwell considers the effect of the motion of the medium on the elec- tromotive force ; he shows that the electromotive force parallel to the axis of X where u, v, to are the components of the velocity of the medium conveying electric action. Here \p is not the electrostatic potential merely; it is equal, as Helmholtz has shown,' to the electrostatic potential plus the term Fu + Go + Hw. We must remark here that ti, v, lo are the components of the velocity of the medium conveying the electric action, i.e. the ether, and this need not necessarily be the same as the velocity of the dielectric. V. Helmholtz' s Dielectric Theory. V. Helmholtz, in the paper ^ to which we have so often referred, con- siders the effect of the polarisation of the dielectric ; he supposes that when an electromotive force X, parallel to the axis of «, acts on an element of a dielectric, it puts it into such a state that it produces the same effect as if there were electricity of surface-density x oii the face dy dz of the element, and an equal quantity of electricity of the opposite sign on the parallel face, x being given by the equation the variations in the electromotive forces acting on the dielectric are supposed to produce the same effect as ordinary conduction currents whose components are x, g, ^, where x, g, 5 are the components of a vector quantity which in isotropic media is parallel to the electromotive force and equal to the product of e and the intensity of the force. This agrees with Maxwell's assumption, provided £ = K/47r, where K is the specific inductive capacity of the dielectric. If <^ be the electrostatic potential of the free electricity, ;// the potential due to the polarisation of the dielectric, then Helmholtz shows that + A |(l + 4;re)A(0-l-,/.) J=-4tE, where E is the volume-density of the free electricity. The corresponding equation in Maxwell's theory is of the same form, provided l-f- 47r£ = K. ' Ueher die Theorie der Elehtrodynainih ; die eleJtirodynamisic'he Krdfte in hewegteJi Leitern, Crelle, Ixxviii. p. 309 ; Gesammelte WerJte, ii. p. 745. ' Ueber die Theorie der EleMrodynamik, Crelle, Ixxii. p. 57; Gesammelte WerTie, i. p. 644. 134 EEPOET — 1885. This relation seems inconsistent with the previous one ; it may, how- ever, be reconciled with it in the following way : — The potential dae to a quantity B of electricity at a point distant r from it is proportional to E If £o be the value of e for air, the potential under the same circumstances in air is proportional to E (l + 47reo)r' if, then, we define unit potential as the potential at unit distance from unit of electricity in air, the potential due to a quantity E in another medium will be r l + 47r£p -1 E 1 l + 47r£ J r' We see that this is equivalent to increasing the unit of potential, and therefore the unit electromotive force, l+47r£o times, so that if we use the new unit the equations will be ^~l+47reo ' d r l+47r£ cl ,^1 = -47rE. These will coincide with Maxwell's equation if we make £ and cq each infinite and put K=£/fo. Returning to Helmholtz's theory, if u, v, w are the components of the total current u=p + x, where p, q, r are the components of the conduction current. Helmholtz puts du dv div dp dx'^dy '^dz~~dt' where p is the volume-density of the free electricity, and if <t be the surface-density of the free electricity at any point of a surface separating two media, ^^l, Vi, w-^; u^, v^, Wa the components of the current in the two media, I, m, n the direction cosines of the nonnal to the surface drawn from the first medium to the second, then according to v. Helm- holtz According to Maxwell the corresponding equations are du dv dw dx dy dz ' I (ui—U2)+m (vi—Vo)+n (iOi—W2)=0. ON ELECTBICAL THEORIES. 135 As it is in the difference between these equations that the difference in the theory really lies, it will be instructive to look at them from another point of view. We know of no way in which the quantity of free electricity can be altered except by electricity being conveyed by con- duction cux-rents to the place where the alteration takes place. Assuming, then, that the alteration in the density is caused by such currents dp dq dr dp l^'^~d~y'^Jz~~di' I (Pi-P2)+m (2i-22)+« (ri-r2)=^. So that Helmholtz's equations taken in conjunction with these are equivalent to the condition dx dy dz ' Thus on Helmholtz's theory the dielectric currents behave like the flow of an incompressible fluid, while on Maxwell's theory it is the total current, which is the sum of the conduction currents and the dielectric currents which behave in this way. The equations we have arrived at for the dielectric currents seem inconsistent with Helmholtz's definition of them ; for since X=eX, with similar equations for p and 3, and since in a medium at rest dt dx' dt~dy' _dW_d(l, dt ~dz' where U, V, W are the components of the vector potential. If we consider a surface separating two portions of the same dielectric and coated with electricity whose surface-density is o-, we have, since U, V, W are not discontinuous on crossing the surface, d r d<t> dm ddr\2 td<t) d(t> cZrf>"|2 I ^ + m j-+n y denotes the difference between the values d(b d^ d<j> of I -J- + WT" + n -T~ on the two sides of the surface. ci3J ciy dz rU d<b d<t,f 1 e da so that I {±^-x^)^m {■Qi-'Q^')^'^ (3i-32)=l+4;re dt^ and so cannot vanish if the surface-density of the electricity changes]; 136 REPORT — 1885. thus Helmholtz's equation seems to be inconsistent with the principle that the change in the quantity of free electricity is caused by conduction currents. In the case above considered, Maxwell's equations lead to no difficulty ; it does not follow, however, that Maxwell's assumption that the total current behaves like the flow of an incompressible fluid is absolutely necessary. We shall consider later on the differences which the abandonment of this assumption will make in the theory. We shall now go on to consider Helmholtz's equations and compare them with the corresponding ones in Maxwell's theory. The quantities U, V, W are given by equation of the form U=J ^^'-<t^\[ —d'E, dt) d^, r where h is the constant which we mentioned before as occurring in Helmholtz's theory, and where <f> is the electrostatic potential ; it follows from these equations that dJJ.dVdW , dd> - — T — — r — ^j — Ic ~i-. ax ay dz dt The corresponding equation in Maxwell's theory is dx dy dz ' 60 that these equations coincide if ^=0. We can see from the value of x given on page 116 that, on Helmholtz's theory, this quantity would also vanish, whatever be the value of k, if the total current behaved like the flow of an incompressible fluid. If a, /3, y are the components of the magnetic force, then on Helm- holtz's theory ay dz Idtdx • J dy dz dx I dtdy J dx dy idtdz J where A is a quantity depending on the unit of current adopted, and is such that the force between two parallel elements of currents at right angles to the line joining them is l-^ijdsds', where r is the distance between the elements, ij the current through them, and ds ds' their lengths ; the corresponding equations on Maxwell's theory are dy_dl3 _, dy dz with similar equations for v and w. ON ELECTRICAL THEORIES. 137 If X, n, V are the intensities of magnetisation, ■& tlie coefficient of induced magnetisation, the equations satisfied by the components of the dielectric and magnetic polarisation are of the type __4^r^(l±M)__A2^+ r ^ _ (l + 4:r^)(l + 4:r0 "1 d_ (i+47r£o) (l + 47rSo) dfi \ k I dx 1 dx dy dz J ^ ~ (l + 47r£o) (1+477^0) ■^' -where eq ^^^ ^0 ^re the values of e and S for air. These equations show that the dielectric and magnetic polarisations are propagated by waves. For the dielectric polarisation longitudinal waves are propagated with the velocity 1 ; (l+47rO (I+^tteq) (l + 47r5o) \l. A I 47r£/j J Transverse waves are propagated with the velocity -V2 + 4;r£o) (l+47r^o) 47re (l+47r3) Longitudinal waves of magnetic disturbances are propagated with an infinite velocity, and traverse ones with the same velocity as the transverse waves of dielectric polarisation. The electrostatic potential is propagated with the velocity IjAs/k. In Maxwell's theory the corre- sponding equations are where fx is the magnetic permeability and K the specific inductive capacity, so that for both dielectric and magnetic polarisation the velocity of the longitudinal wave is infinite, while the velocity of the transverse wave is l/s/fiK. The velocity of propagation of the electrostatic potential is infinite. If in Helmholtz's theory we put Z;:=0, •&o = 0, £/£o=K, while both £ and £0 are infinite, we see that the results of his theory will in this respect agree with Maxwell's. Though in Maxwell's theory the velocity of propagation of the electro- static potential is infinite, and in Helmholtz's theory 1/A\/A;, the electro- motive force at a point, and consequently the dielectric polarisation, does not travel with an infinite velocity in Maxwell's theory, or with the velocity 1/A\/ A; in Helmholtz's. We can see the reason of this nacre easily from Maxwell's theory, as the equations are simpler. Using the notation of that theory, viz.,/, g, h, for the components of the electric displacement, F, G, H for the components of the vector potential, and ^ for the electrostatic potential, then in a dielectric the equations are 4<-rr . _ _ d¥ _ d(p K^ ~ ~dt "dx 138 EEPORT— 1885. 477 df_ _ tPF _ d^ 'K dt~ 'dF' dxdt' but, since 47r/i ^= — v ^F, we see that ±^v^F='^ + ^. fi\L d.f' dxdt Now, since v ^^ = 0, a particular solution of tWs differential equation will be dt dx while the general solution will be the sum of this solution and the general solution of /iK dt^ The particular solution is propagated at the same rate as f, while the other part of the solution represents a wave travelling with the velocity 1 / V^K. Since the part of the solution which travels at an infinite rate satisfies the equation dt dx or f= 0, we see that the electromotive force due to the change in the vector potential just balances the electrostatic electromotive force, so that until the part of the vector potential which travels at the rate Ij s/fjiK comes up the resultant electromotive force vanishes. This explains how the electromotive force on Maxwell's theory travels at a different rate from the potential, and a similar explanation will apply to Helmholtz's theory. Helmholtz's equations for a conductor are a^hc= (1 +47r^) 47rA2 f^-^^ { V> + (1 + 4,r^-/.-) A^ || } where a is the specific resistance of the conductor ; on Maxwell's theory the equations are 9 J du These equations differ by terms involving the unknown constant h; but V. Helmholtz's ' investigations on the motion of electricity along thin conducting wires show that there is not much hope of distinguishing be- tween the theories by experiments on conductors. We have seen that we can make certain equations which occur in Helmholtz's theory coincide with the corresponding ones in Maxwell's by giving par- ticular values to certain constants. The difference in Helmholtz's and Maxwell's views as to the continuity of the currents is too serious to let us expect that we should ever get a complete agreement between the ' Zfeher die Ben-egvngsgleichxmgen der Elehtricitdt fiir ruheiide leitende Korper. Gesammelte Werke, vol. i. p. 603. ON ELECTRICAL THEOKIES. 139 theories ; and, in fact, make as many assumptions about the constants as we may, there are still differences between the theories. In order to get as general a theory of these dielectric currents as possible, we shall investigate the consequences of assuming merely that these currents are proportional to the rate of change of the electromotive force, and write dielectric current^ r; (rate of change of the electromotive force), where ?/ is a constant which for the present is left indeterminate; In Maxwell's theory 7;=K/4n-, where K is the specific inductive capacity of the dielectric ; in Helmholtz's theory, i] is also proportional to the spe- cific inductive capacity. We shall denote the components of the dielec- tric currents by the symbols f, g, h; the components of the conduction current by p, q, r, and the components of the total current by ii, v, w, so that u=p +/. Let us put du , dv dw p dx dy dz ' I (ui—U2) + m (vi—V2) + n (wi—W2)=:^ ; on Maxwell's theory I" and 2 are each zero. If F, G, H are the components of the vector potential, then by V. Helmholtz's investigation of the most general expression possible for these quantities consistent with the condition that the forces between closed circuits should agree with those given by Ampere's laws, • ¥ = i(l-k)^+f.{{{'td^dnd^, with similar expressions for G and H, where Jc is a constant and Transforming this expression we see, using the same notation as before, that 1/'= rfi{l («! — 1^2)+™ (yj— Vo)-!-^ (^1— ^^2)} ^^ = fLrS(iS- {{ fir P d^ dr, di;, where dS is an element of a surface at which there is discontinuity in u, V, w. Let us now consider the equations which hold in a perfectly insulating dielectric. The rate of change of the x component of the electromotive force in a medium at rest = _^ _ d^(p dt^ dt dx* where ^ is the electrostatic potential ; it also equals // rj, so that f__d^F_ d^(t> H dt'^ dt dx 140 BEPOET — 1885. Since in this case there is no conduction current u =/, and the pre- ceding equation for F shows that substituting for/ if - — 1- , + -— - = Y, we get, by dififerentiating this expression, ax ay az ^ <=> •' with regard to x and the corresponding equations for G and H with regard to y and z respectively, and adding v=^x - i (1-^) vV = 4x,;x|A^X + I V^^ } . Now, as the dielectric is a perfect insulator, there are no conduction currents, so that the density of the free electricity remains constant, and therefore From the expression for yp we see that Substituting this value of v^J' in the equation for x, we get which represents the propagation of a normal wave with the velocity 1/ V^Trrjk. The transverse wave is propagated with the velocity l/v4rr)7/j, so that if the view that light consists of electric or magnetic disturbances be correct, since experiment shows that this velocity is very nearly equal to l/'^Kfj., we must have 47rj; = K or ?j = K/47r, which is Maxwell's theory. So that if we assume that light is_an electric phenomenon, then in those mediain which its velocity = 1/n//uK Maxwell's theory that the electric cui'rents flow like an incompressible fluid must be true. If a, /3, y are the components of the magnetic force, then, since 4 F = 1 (1 - z;) ii + Mi'i m dr, di;, we see from Ampere's formula for the magnetic force due to a circuit that ^^dH_dG _ dY dy dz dz ' ON KLECTRICAL THEOKIES. 141 where V is the magnetic potential due to the magnetism in the field both permanent and induced. From these equations we get I dy dx j dz\. d.v dy dz J = _ 4;r,,i«+ ^ |i (1 _ /,) V^v^ - x} instead of the equation da dS . -— — = — 4!Trw. ay dx We have been obliged to introduce another assumption|liere, viz., that the magnetic force due to an element of current is given by Ampere's expression. We could not assume Maxwell's way of connecting currents with magnetic force, viz. that the total current flowing through any closed curve is equal to the line integral of the magnetic force round the curve, for the result can only be true when the currents flow like an incom-' pressible fluid. Let us now go on to consider the force acting on the medium convey- ing the current. If we consider a continuous distribution of currents, the kinetic energy — 2 i i (F2i + Qv + B.w) dx dy dz. If we derive the force parallel to x by the variation of the energy in the usual way we find, just as in Helmholtz's paper, • that the force parallel to x I \dx dy) \dx dz) \dx dy^dljr or with our notation = V < \ dx dy J \ dx dz J ' and that on any surface where there is a discontinuity in the values of u, V, w there is a force equal per unit of area to F [I («i — u^) + m (i^i — v^) + n (w, — w^)} or F2. In the same paper it is shown that it follows from the principle of the Conservation of Energy that the force exerted by a distribution of cur- rents equals the force given by Ampere's expression along with a force at the point ^r)l^ whose component parallel to the axis of x equals \\\ (S + I ^ 1^) ^ (^' {^-^) + ^' (y - v)+w' (z-Oyxdydz ■* J J V ^^' ~ "^'^ ■*■ '" ^^' ~ "^2) + '^ (^1 - ^i) ] ^-^^ G<'' (aJ - > Die eleUrodi/namischen Kr'dfte in hewegten Lcitern, Crelle, Ixxviii. p. 298 1874, or Gesammelte Werke, vol. i. p. 733. 142 itEPOET— 1885. or with our notation ' "^^ [^1'' {x-D + v' (y - n) + w'(z- O) ^^ dy d^ + W-"" ^T '(^^' («= - + ^' (y -v) + w' (z- o) ds, where u', v', w' are the components of the current at the point ^ rj ^; so that in addition to Ampere's forces we have additional forces wherever P and S have finite values. From the above expressions we see that any element where P has a finite value exerts a repulsive force equal per unit of volume to — ^ cos 6, r tending from the element ; where r is the distance of the element from the point at which the force is reckoned, i the intensity of the current at this point, and 6 the angle between the direction of the current and r. Any element of surface where S has a finite value exerts a repulsive force equal per unit of surface to V ~' i cos y, r where the notation is the same as before. Of course none of these forces exist in Maxwell's theory. They could be most easily detected in cases where the part of the forces given by Ampere's theory vanishes as it would for the case of an endless solenoid. In this case, though the Amperian forces vanish, the forces due to the discontinuity in the current do not, so that if the endless solenoid were to move under the action of external currents it would denote the existence of discontinuity in the current. An experiment of this kind has been made by Schiller ; we shall discuss the results of it later. To sum up, the differences between the most general theory which takes into account the action of the dielectric, and Maxwell's, are — 1. The existence of a normal wave in the general theory, but not in Maxwell's. 2. The difference in the velocity of propagation of the transverse wave. 3. The difference in the relation between electric currents and mag- netic force. 4. The forces which arise from discontinuity in the currents. The Experimental Evidence as to tlie Truth of the various Theories. The theories we have considered may be divided into two great classes, according as they do or do not take into account the action of the dielec- tric surrounding the various conductors in the field. The first thing, therefore, that we have to do is to see whether experiment throws any light on this point. When a dielectric is in an electric field it experiences a change in its structure ; this is rendered evident by the alterations in its volume and elasticity observed by Quincke, by the change in its optical properties \ ON ELECTKICAL THEORIES 143 observed by Kerr, and also by the fracture of the dielectric when the field is made sufiBciently intense. So that whenever an electromotive force acts on a dielectric it produces a change in its structure which we shall always speak of as polarisation. This, strictly speaking, has only been directly proved for electromotive forces produced by charges of statical electricity ; but, unless we are prepared to say that the electromotive force due to statical electricity is in some way different from that due to a changing current, we must admit that when an electromotive force of the latter kind acts on a dielectric it polarises it. And we are not with- out experimental evidence that the electromotive force due to variations in the vector potential does produce some of the effects of the electromo- tive force due to a charge of statical electricity. Rowland's experi- ments have shown that a moving electrified body will set a magnet placed near to it in motion. It follows from this, by dynamical prin- ciples, that if we have the charged body initially at rest and move the magnet it will, if no other forces act upon it, be set in motion ; so that in this case there is an electromotive force due to the motion of the magnet, i.e., the variation in the vector potential produces the same effect on the electrified body as the electromotive force due to a charge of statical electricity. For this reason we shall suppose that the electro- motive force due to the variation in the vector potential always produces effects on a dielectric on which it acts of the same type as those which have been observed to arise from the action of an electromotive force due to a charge of statical electricity. Let us now consider a magnet surrounded by a dielectric. If we set the magnet in motion, we produce an electromotive force which polarises the dielectric. Let us, to fix our ideas, consider an element of the dielec- tric and the magnet. When the magnet moves it polarises the dielectric ; it follows from dynamical principles (an extension of the principle of action and reaction),' that if the polarisation of the dielectric be altered, the magnet will move, so that a change in the polarisation of a dielectric produces a magnetic force. Again, let us instead of the magnet consider a coil of wire conveying a current. A change in the rate of flow of the current produces a change in the polarisation of the dielectric ; it follows that a change in the rate of change of the polarisation of the dielectric will produce a change in the current, i.e., will produce an electromotive force. It follows too, from dynamical principles, that as the change in the polarisation of an element of the dielectric due to the change in the current depends on the distance of the element from the current, there must be a force between the current and the element when the polari- sation of the latter is changing. Thus we see that a change in the polarisation of the dielectric must produce all the effects of an ordinary conduction current, so that it is only absolutely necessary to consider how the experimental evidence affects those theories which take the action of the dielectric into account. As, however, the experiments which have been made are few in number, and are all concerned with interesting points, we shall consider them in their relation to all the theories, and not only to those which take the dielectric into account. ' See a paper by the author of this report ' On some Applications of Dynamical Principles to Physical Phenomena,' P/dl. Trans., 1885. 144 EEPORT — 1885. Schiller's Experiments. The first experiment whicli we shall discuss is oue made by Schiller^ and described by him in Poggendorf s Annalen, vol. clix. pp. 456, 537 j it was intended to test the potential theories of Neumann and Helm- holtz. We saw that, according to these theories, in an unclosed circuit there are, in addition to the forces due to the elements of current, and which are expressed by Ampere's law, forces arising from the discon- tinuity of the currents at the ends of the circuit. If we have an end of a circuit where the current stops, and the electricity accumulates at the rate dejdt, it will exert on an element of current of length ds traversed by a current of intensity i a force tending to the end and equal to i 2 • 7 de cos Q * * 'Jt ^r where is the angle between the element of current and the radius drawn to it from the end. If we calculate from this expression the couple pro- duced by an end on an endless solenoid, or on what is practically the same thing, a ring magnet, we shall find that the couple tending to turn the ring about an axis in its own place will not vanish, while the couple arising from the forces given by Ampere's law will. Thus if the ring rotates, as it should according to the potential theory, it must be from the action of the end. In Schiller's experiment the end of the current was the end of wire connected with a Holtz machine. This was placed near to a ring magnet which was suspended by a long cocoon fibre ; the magnet was protected from electrostatic influences by being enclosed in a metal box connected with the earth. Schiller determined the intensity of magnetisation of the ring magnet and the quantity of electricity passing through the point, and he calculated that if the potential theory were true, he ought to get a deflection of the magnet of about 27 scale divisions, instead of which there was no perceptible deflection. This experiment shows conclusively that the potential theory is wrong if we neglect altogether the action of the dielectric, and assume the cur- rent to stop at the end of the wire. If, however, we take the dielectric into account, the experiment tells us nothing as to whether Maxwell's theory or the more general one is true ; for since the current from the Holtz machine is steady, as much electricity flows out from the end of the wii'es as arrives there ; and thus there is really no discontinuity in the current, the only difference being that before reaching the end the current is flowing through copper and after passing it through air. The condition of things at the end of the wire remains steady, and thus the quantities which we denoted by P and 2 vanish. The experiment might, however, be modified so as to be capable of distinguishing between the theories which take the dielectric into account, For suppose that, instead of letting the electricity escape through the point, we never let the potential at the end of the wire get so high as to allow the electricity to escape ; then if the wire is initially uncharged, the condition at the end will be changing whilst the wire is charging up, and thus 2 will have a finite value ; so that if the magnet were sufficiently delicate and remained undeflected, whilst the point was surrounded by dielectrics of all kinds, it would show that Maxwell's theory is correct. I have calculated the effect which would be produced on Schiller's ON ELECTRICAL THEORIES. 145 suspended magnet, and find that it is too small to be observed ; as, bow- ever, the time of charging up the wire will be very small compared with the time of vibration of the magnet, the effect will be of the nature of an impulse, so that in this case there will be considerable advantage in having the moment of inertia of the suspended magnet small ; while, as Schiller arranged the experiment, there was no such advantage, as the thing expected was a steady deflection. Thus if the ring magnet were retained it would be desirable to make the opening of it as small as pos- sible, retaining the same cross action. I think the arrangement could be made sensitive enough to be deflected if the value of S were any considerable fraction of the rate of increase of the electricity at the end of the wire. There is another way in which the continuity or discontinuity of the current might be tested, and which might perhaps be more delicate than the last. We saw on p. 141 that at any point of a current at which S had a finite value the mechanical force on the element is not at right angles to the element. In addition to the ordinary force at right angles to the element, there is a force in the direction of the vector potential equal in magnitude to the product of the values of the vector potential and 2. The existence of this force could be tested by an arrangement of the following kind : — AB and CD are light movable segments of the same circle, having balls covered with paraifin A, B, C, D fastened to their ends. These segments are connected with a very light framework which can rotate about an axis per- pendicular to the plane of the segments ; the segments touch at their middle points contact, pieces which are connected with a Holtz ma- chine. EP is the section of an electromagnet concentric with AB and CD ; the whole is surrounded with a metal cylinder to screen it from external electric influences. When a curi'ent is passing through the electromagnet it produces a vector potential, whose direction is at right angles to the radius from O, the centre of the electromagnet perpendicular to its axis. Thus if 2 exists there will be a couple tending to twist the system AB, CD about its axis, but if S exists at all it will be when the electrical condition of the balls A, B, C, D is changing, so that unless the currents are continuous we should expect the system to rotate when the balls are being charged up. I have calculated that the system might easily be made sensitive enough to be sensibly deflected on charging or discharging, pi'ovided 2 is an appreciable fraction of the rate of change of the surface-density of the electricity on the balls. Schiller's Secojid Experiment.^ Schiller has made another experiment, which shows that Ampere's theory fails for unclosed circuits. The first form of the experiment con- sisted in having a solenoid placed over a condenser one of whose plates could rotate about a vertical axis coinciding with the axis of the solenoid. One end of the solenoid was connected to one plate of the condenser and the other end to the other plate. When the solenoid is connected to a ' Pogg. Ann., clix. p. 456; clx. p. 333. 1885. L 146 KEPOET— 1885. battery the condenser will charge up and there will be radial currents of electricity in the plates ; the current passing through the solenoid will produce a magnetic force which will, if Ampere's theory be true, act on the radial currents in the plate of the condenser and set it in rotation. Schiller found that this effect was too small to be observed, so he modi- fied the experiment in the following way. Let us suppose that we have the two plates of the condenser rigidly attached to their axis and placed in a field symmetrical about its axis, in which the vertical component of the magnetic force is not uniform. Then if a current be sent through the upper plate, down through the axis, and out at the lower plate, the couple tending to twist the lower plate will not be equal and opposite to that tending to twist the upper one, as the magnetic force is not equal at the two plates, and thus the condenser will be set in rotation. Con- versely, if the condenser be set in rotation in the magnetic field, and two electrodes of a galvanometer be connected with its axis, then if Ampere's theory be trne there will be an electromotive force acting round the galvanometer circuit, which will produce a current, and this current could be much more easily detected than the rotation in the first form of the experiment. Schiller calculated the deflection which he ought to get if Ampere's theory were true, and found that he could easily detect it if it existed ; as he was not able to see any deflection, we must conclude that Ampere's theory is not the true one. It is easy to see that, according to the potential theory, there would be no curreutin the galvanometer ; for, as everything is symmetrical about the axis, the potential is not altered by the rotation. The following calculation will show that, according to the dielectric theories, there should be no current through the galvanometer. For if a, b, c are the components of magnetic induction, F, G, H those of the vector potential, X, Y, Z those of the electromotive force, then dt clt dx \ dt dt dt J „ dz dx d ^ -rj, dx p dy , -ri clz\ ^ = "^1- ' dt'dyV It-^ ^ '^dt''^ dt] i Suppose the condenser is rotating with an angular velocity w about the axis of Z ; then the E.M.F. arising from one plate is, if E, be its radius, '^0 -'-(^-S+«t)- Now F ^ -h G I' = ..Re, dt at where is the component of the vector potential along the direction of motion of a point on the circumference of the plate of the condenser. But the line integral of the vector potential round any curve equals the number of lines of magnetic force passing through it, so that, since the field is symmetrical, .R 27r cr dr = 27rRe. ON ELECTRICAL THEORIES. 147 From this equation we see that the E.M.F. due to the rotation vanishes for each plate, so that, according to this theory, there should be no current through the galvanometer. This experiment of Schiller shows that both Grassmann's and Clau- sius' theories must be wrong, as well as Ampere's and Korteweg's, for we can easily see that they would make the disc rotate in the way in which Schiller first tried the experiment, and if this were so, it follows from dynamical principles that a current must be produced in the second form of the experiment. This would seem to be the case even if we take into account the cur- rents in the dielectric, unless we suppose that all the circuits are closed, for if all the circuits are closed then the disc will not rotate, as all the theories agree. If the circuits are not closed we may divide the currents in the disc into two parts, one part being of such magnitude as to form with the dielectric currents closed circuits ; then the forces on this part and the dielectric will form a system in equilibrium ; and there remains the other part of the currents, the action of the magnet on which ought to set the disc in rotation. Taking Schiller's experiments together, we may say that they show that the dielectric must be taken into account, and that some form of the potential theory is the only one of the theories we are considering which can give the expression for the forces due to a distribution of currents. Although these two experiments of Schiller's show that of the theoi'ies we have discussed only the dielecti'ic ones can be retained, we shall describe one or two more experiments which have been or could be made to distinguish between the various theories. Clausius' and Grass- mann's theories lead to the same expression for the force between two elements of current, so that these theories stand or fall together. Grass- mann in his paper ^ describes an experiment which would distinguish between his theory and Ampere's, or, in fact, any other except Clausius' which has ever been published. Suppose that NS and SN" are two mag- nets whose north and south poles are de- noted by N and S respectively, and that these magnets are fastened together by a rod NS, the system being suspended by a cocoon thread attached to the middle point of NS. Let AB be an unclosed circuit, say a wire joining the plates of a charged con- denser ; then, according to Grassmann's and Clausius' theories, the system will rotate in such a way that the sense of rotation is re- lated to a vertical line drawn downwards like rotation and translation in a right- handed screw. According to every other theory it will rotate in the opposite direction. Another experiment has iDeen made by v. Helmhoitz,^ which shows that the potential theory leads to wrong results unless the action of the dielectric is taken into account, hh is a rotating conductor, to the ends of which large condenser plates are attached, which, when in rotation, come very near to the similar plates c, c. The plates h and c are segments s N Pogg., Ixiv. 1, 1845. WissensohaftlicJie Ahhandhmgen, vol. 783. L2 148 EEPOKT — 1885. of coaxial cylinders. lu v. Helmholtz's experiments bh was rotated between the poles of a powerful electromagnet. The plates c, c were connected with a commutator, which put them to earth when the rotating piece was in the position A, and to the plates of a Kohlrausch condenser when it was in the position B. Now suppose there is a difference of potential between h and c ; suppose, for clearuess, that 6 is at a higher potential than c, then when the rotating piece is in the position A the positive electricity goes to earth, and the negative is left to go to the Kohlrausch condenser, when the rotating piece gets to the position B. The change in this condenser was measured by a quadrant electrometer. V. Helmholtz found that the needle of the electrometer was deflected when the piece hh was rotating. Since everything is symmetrical about the axis of rotation, there would be no difference of potential between the plates h and c, according to the potential law, if we neglect the action of the dielectric. According to Ampere's law there will be a difference of potential between h and c equal to Qmo, whei'e a is the radius of the rotat- ing piece, w its angular velocity, and 9 the vector potential along the direction of motion of the disc. According to the dielectric theory there will also be the same difference of potential between h and c if we sup. pose that there is no discontinuity in tbe motion. We shall suppose that, instead of the velocity changing abruptly from (oa to zero as we pass from the rotating conductor to the dielectric, there is a layer of the dielectric next to the conductor in which the change of velocity is very rapid, one side of the layer moving' with the velocity wa, the other side being at rest. Then, using the same notation as before, we have — '—. '^1/ -h'k. __ . — , ^ (It dx\" clt ' ^ dt ' " dt X=c dt dy L dt dz dx q(7^/ dt dt + H dt } I Integrating across the thin layer of the dielectric, in which the velocity is changing rapidly, we see that the difference of jDotential between b and c equals where dxjdt, dijjdt, dzjdt are the velocities of a point on the boundary ON ELECTRICAL THEOEIES. 149 of the moving conductor. This equals Qaw, the same value as that given by Ampere's theory, so that in this case the two theories lead to identical results, which are in agreement with the result of Helmholtz's experiments. Rontgen has recently published ' a preliminary account of some experiments which seem to pi'ove directly that the variations in the dielectric polarisation produce eflPects analogous to those due to a current. This completes the account of the experiments which have been made to test the various theories. As the result of them we may say that they show that it is necessary to take into account the action of the dielectric, but they tell us nothing as to whether any special form of the dielectric theory, such as Maxwell's or Helmholtz's, is true or not. I have described two experiments which would decide whether Maxwell's theory that all circuits are closed is true or not. It seems to me, however, that even if Maxwell's theory be wrong, Helmholtz's is not the only alternative. I have given a sketch of a theory in which I have tried to make as few assumptions as possible ; all that I have assumed is that when a dielectric is acted on by a changing electromotive force, it behaves like a conductor conveying a current whose intensity is pro- portional to the rate of change of the electromotive force. We know from experiment that it produces effects of the same character, and I have assumed as the simplest assumption I could make that for the same dielectric the equivalent current is proportional to the rate of change of the electromotive force, so that equivalent current = r/ (rate of change of electromotive force). Both Maxwell and Helmholtz assume that rj depends only on the specific inductive capacity of the dielectric, but I think it is preferable, until we have more experiments on this point, to look on r) as the measure of a new property of a dielectric, and not to assume that it is merely a function of the specific inductive capacity, the only experimental evi- dence for this being the by no means perfect agreement between the refrac- tive index and the reciprocal of the square root of the specific inductive capacity. To prove Maxwell's theory of closed circuits it would not be sufiicient to prove that for one medium, say air, r; =::■ K/47i-, for it is quite conceivable that electrical phenomena may be simpler in a dielectric like air, where the electrical behaviour of the ether seems to be but little affected by the presence of the dielectric, than in such a one as glass or other substance possessing a comparatively large specific inductive capacity, when the effect of the ether is seriously modified by the presence of the medium. Since in the theory I have sketched the values of du d V dvj dx dy dz and I (it, — ^(2) + in (u, — v^) + n (wj — iv^) are not zero, but arbitrary, inasmuch as they involve ?;, in order to find the value of the force between two circuits where there is any dis- continuity in the currents we shall require to know the value of the quantity k which occurs in v. Helmholtz's theory. The most pressing need in the theory of electrodynamics seems to ' Phil. Mag., May. 1885. 150 EEPOET — 1885. be an experimental investigation of the question of the continuity of tliese dielectric currents ; we have experimental proof that they exist, but we do not know whether Maxwell's assumption that they always form closed circuits with the other cui'rents is true or not. If Maxwell's assumption should turn out to be true, we should have a complete theory of electrical action ; if, on the other hand, it should turn out to be wrong, then we should have to go on to determine the quantity h. This quantity is diffi- cult to determine, as its influence on all closed circuits disappears. It influences, as v. Helmholtz has shown, the rate of propagation of the electric potential along conducting wires, and I think we can see that it would influence the time of oscillation of an irregular distinbntion of elec- tricity over a conducting shell. The easiest way, however, of determin- ing this quantity would seem to be the straightforward one of measuring electrostatically the value of the electromotive force due to a valuation in the charge of a condenser ; the expression for the vector potential, as we saw on p. 140, involves h, so that if we measure the electromotive force, which is equal to the i-ate of variation of the vector potential, we shall determine the value of the vector potential, and consequently of Ic. Appendix I. Since the Report was written I have had through the kindness of the author an opportunity of seeing the advance proofs of a paper by Pro- fessor J. H. Poynting, of Mason's College, Birmingham, ' On the Connexion between Electric Current and the Electric and Magnetic Induction in the Surrounding Medium,' which is about to appear in the ' Philosophical Transactions.' The views expressed in this paper are rather a new way of looking at Faraday and Maxwell's theory than a new theory of electrodynamio action, as however it brings the action of the dielectric into great prominence it is instructive to consider it. The paper is largely based on a previous one by the same author on the ' Transference of Energy in the Electromagnetic Field,'' it is therefore necessary to give a brief account of this paper. In it the author shows that the rate of increase of the energy inside any closed surface equals ^{[{l (R'/5 - Q'y) + m (yF - aW) + n («Q' - /3F)}c?S, where cZS is an element of surface, 1, m, n the direction cosine of the normal to JS, o, /3, y the components of magnetic induction, and P', Q', R' given by the following equations : — p,^_dF_# dt dx* ^ -" dt dif cm chj. ^ ~ dt dz' ' Phil. Trans., 1884, part ii ON ELECTBICAL THEORIES. 151 ■where r, G, and H are the components of the vector potential and xp ^^^ electrostatic potential ; thus if the medium is at rest P', Q', H' are the components of the electromotive force at the point. Professor Poynting interprets this equation to mean that the components parallel to the axes of x, y, z of the flow of energy across each element of surface are respectively 2:(R'^-Q-V), 4ir 1 (Q'« - ?'/3), so that according to this view the energy flows in the direction which is at right angles both to the magnetic and electromotive forces, and in the direction in which a right-handed screw would move if turned round from the positive direction of the electric intensity to the positive direction of the magnetic intensity ; the quantity of energy crossing in unit time unit surface at right angles to this direction being — . Electromotive force at the point X magnetic force X sine of the angle between these forces. This interpretation of the expression for the variation in the energy seems open to question. In the fir.st place it would seem impossible a priori to determine the way in which the energy flows from one part of the field to another by merely differentiating a general expression for the energy ill any region with respect to the time, without having any knowledge of the mechanism which produces the phenomena which occur in the electromagnetic field : for although we can by means of Hamilton's or Lagrange's equations deduce from the expression for the energy the forces present in any dynamical system, and therefore the way in which tlie energy will move, yet for this purpose we require the energy to be expressed in terms of coordinates fixing the system, and it will not do to take any expression which happens to be equal to it. The problem of finding the way in which the energy is transmitted in a system whose mechanism is unknown seems to be an indeterminate one ; thus, for example, if the energy inside a closed surface remains constant we cannot unless we know the mechanism of the system tell whether this is because there is no flow of energy either into or out of the surface, or because as much flows in as flows out. The reason for this diff'erence between what we should expect and the result obtained in this paper is not far to seek. Though tlie increase in the energy inside a closed surface equals i||{KR'/3-Q'r) + . • • -l^S, it does not follow that the components of the flow of energy across each element of surface are (R'/j — Q'y)/^'!', &c., for we can find quantities u, V, IV which are of the dimensions of rate of change of energy per unit area, and for which (lu + mv + niv) dS := 0. u ■ 152 EEPORT — 1885. The following values of u, v, iv satisfy this condition : — = 1 / JL. (FG) - -^ (HF) \ , t, = i ( JlL^ (GH) - -^ (FG) 1 , w = ^( /^' (HF) - f\ (GH) ], fj.ldx dt ^ ^ dijdt^ ^ r where /x is the magnetic permeability and F, G, H are the components of the vector potential, or if i// be the electrostatic potential «=^{#hJ-,^{^^g1, dy L dz J dz [. dy J dy L dz J dz {. dy . = ^(l^FJ-^(i^Hl, dz L dx i dx I dz J ^„=i.(^G"i-^{^^p"l, (/a; L t'y J dy [. dx J If the values of u, v, w which satisfy these conditions be denoted by the («!, ^1, w{), {u^, V2, w^ . . . then the flow across any element of surface might have for its x component — ~(R' ft - Q' y) + Xi «, + Xo u, + \3 % + . . . where X,, Xj, X^ are arbitrary constants, thus we see that the components of the flow of energy, instead of being uniquely determined by this pro- cess are really left quite indeterminate by it. Though this is so, it is very instructive to follow Professor Poynting's description of the way in which the energy flows in some special cases ; we shall select a very simple one, the case of a current flowing along a straight wire. Here the lines of electromotive force are straight lines parallel to the wire, the lines of magnetic force are circles with their centres on the wire, and their planes at right angles to it. Then, since according to the view expressed in the paper, the energy moves at right angles both to the electric and magnetic forces, it must in this case move radially inwards to the wire where it is converted into heat. The energy, instead of being supposed to be transmitted through the wire, is regarded as transmitted by the dielectric ; and though we may not regard the exact law of flow of the energy as established, still it is very important that this view should be brought into prominence. Another important point brought prominently forward in this paper is the view that magnetic force is always the sign of transference of energy, according to Professor Poynting ; indeed, there must be transference of energy from one part of the field to another to give rise to magnetic force. Thus, according to his view, no magnetic force would be exerted by the discharge of a leaky condenser, because in this case he considers the energy to be confined to the space between the plates of the condenser and to be converted into heat where it stands. If the plates were connected by a metallic wire, the energy could flow out and be converted into heat in the wire and this motion of energy would give rise to magnetic forces, so that magnetic ON ELECTRICAL THEOEIES, 153 forces wonldbe produced by the discharge of a condenser in this way, but not by leakage. In this case the theory differs from Maxwell's, as according to that theory the alteration in the electromotive force w,ould produce magnetic forces in either case. In Professor Poynting's second paper, which we have already men- tioned, the fundamental principles of electrodynamics are described as the results of the motion of the tubes of electromotive and magnetic force. Maxwell develops electrodynamics from the principles : — 1st. That the total electromotive force round any closed curve is equal to the rate of decrease of the total magnetic induction through the curve. 2nd. The line integral of the magnetic force round any closed curve is equal to 4:ir times the current through the curve. Professor Poynting restates these principles in the following way : — 1. ' Whenever electromotive force is produced by change in the mag- netic field, or by motion of matter through the field, the E.M.P. per unit length is equal to the number of tubes of magnetic induction cutting or cut by the unit length per second, the E.M.P tending to produce induction in the direction in which a right-handed screw would move if turned round from the direction of motion relatively to the tubes towards the direction of the magnetic induction.' The second principle he states in the following way : — ' Whenever magnetomotive force is produced by change in the electric field, or by motion of matter through the field, the magnetomotive force per unit length is equal to 47r times the number of tubes of electric induction cutting or cut by unit length per second, the magnetomotive force tending to produce induction in the direction in which a right- handed screw would move if turned round from the direction of the electric induction towards the direction of motion of the unit length relatively to the tubes of induction.' By magnetomotive force is meant the line integral of the magneto- motive force round a tube of induction. This statement includes the more special one that the line integral of the magnetic force round any closed curve is equal to 4m times the number of tubes passing in or out through the curve per second. The development of these principles leads to equations which are practically the same as those obtained by Maxwell, the chief difference being that the quantity corresponding to Maxwell's J is no longer arbitrary or rather redundant. Professor Poynting also introduces into his equations the time integrals of the components of the magnetic force as fundamental quan- tities, and regards the components of the magnetic as the differential coefficients of these quantities with regard to the time. This method of representing magnetic force was also used by Professor Fitzgerald in his paper on the Electromagnetic Tlieory of the Reflection and Refi-action of Light.' It has the advantage of calling attention to the dynamic character of magnetic phenomena. In Professor Poynting's paper some of the applications of his method of regarding electrical phenomena are worked out with great detail for some of the simpler cases. ■ PMl. Trans., 1880, part ii. 1<'54 EEPOET — 1885. Appendix II. ON THE STRESS IN THE DIELECTRIC. In the preceding Report we have had so frequently to refer to the action of the dielectric that it may be convenient to give a very brief ac- count of the work which has been done on the stresses which are sujDposed to exist in it. We shall confine ourselves to the work which has been done on the stresses in the electrostatic field; those existing in the electro- magnetic field are of a similar nature, so that any remark applying to one will also apply to the other. The idea of explaining the forces in the electrostatic field by means of stresses in the dielectric seems to be due to Faraday, who describes ' the stress in the medium by sayiug that the lines of force tend to contract and also to repel one another. The magnitude and distribution of this stress was investigated by Maxwell ; ^ he found that in a medium whose specific inductive capacity was K, and at a point where the electromotive force is E, a tension equal to KR^/Btt per unit area along the lines of force combined with a pressure of the same amount at right angles to these, would produce the effects observed in the electrostatic field, that is, at a point in a dielectric, the resultant of these stresses would be a force whose components, parallel to the axes of X, y, z, are eX, eY, eZ respectively, e being the charge of electricity at the point, and X, Y, Z the components of the electromotive force. It may be observed that this system of stress could not be produced by the strain in an elastic solid at rest : this points to the kinetic origin of "electrostatic phenomena. These stresses are in equilibrium at a point in a dielectric where there is no free electricity. At the junction of two media, whose specific inductive capacities are K, and Kg, and in which the electromotive forces are Ri and Rj, and whose interface is perpendicular to the lines of forces, the stresses are not in equilibrium, but there is an unbalanced stress (Kj Ri" — Ko Rj-) /Stt which will tend to make the boundary move towards the medium whose specific inductive capacity is Kj ; if these dielecti'ies are liquids, their interface may become curved so that the forces due to surface tension balance this stress. Quincke,^ who has experimentally investigated the effects of electrifi- cation on various dielectrics, such, for example, as the efiects on the glass of a Leyden jar, has found that the efi'ects on difi^erent bodies ai-e very different ; he finds, for example, that though the effect of the electrification on the dielectric of the Leyden jar is generally to produce an expansion, yet^ in some substances, such as the fatty oils, contraction takes place.* This diversity in the effects of electrification on different dielectincs shows that the distribution of stress cannot be so simple as was supposed by Maxwell. It also shows that there must be forces in the electric field which are not recognised either by Maxwell's theory or the theory of action at a distance. More general theories have been given in order to meet this difficnlty. ' ExjjeTiiHeiital Eesearchcs, § 1 297. ^ Wectrioity and Magnetism, 2ncl edition, p. 149. 3 Wiecl. Ann., x. pp. l(jl, 374, 513; IMd., ix. p. 105; Pidl. Mag., yo\.:^. n. ZO (1880). I ' J ' I * The fatty oils are also an exception to the rule that the index of refraction equals the square root of the specific inductive capacity. ON ELECTEICAL THKOEIES. 155 T. Helmholtz ' lias supposed tliat a change in the density of a dielec- tric might alter its specific inductive capacity, and he has investigated the consequences of this supposition. Korteweg and Lorberg ^ have investigated the more general case, when the specific inductive capacity of a strained dielectric is supposed to be a function of the strains. Korteweg supposes that if the body suffers dilatation e along the lines of force, and dilatations / and cj at right angles to them, then the specific inductive capacity = K— ae— /3 {f+g)- Helmholtz assumed that a = /3. The presence of strain in a dielectric must influence the specific indiTctive capacity, for Quincke has shown that the various coefficients of elasticity are altered under the influence of electricity. Lorberg, I.e., has found the distribution of stress in the medium when the specific inductive capacity alters in this way. He finds that there is a tension along the line of force equal to and a pressure at right angles to them equal to KStt 2 J The force in the medium parallel to the axis of x where *±7r tCit/ tltl/ tviO tltt' tvU tlAf till + _^ (a-/3) ^^ dz dx dz Where is the potential, and p the volume density of the free electricity. The part A of this force exists even when there is no free electricity at the place under consideration ; if the dielectric were a fluid, these terms would indicate forces tending to move the fluid when placed in a variable electx'ic field ; this motion, however, seems not to have been observed. The supposition made by Korteweg and Lorberg is not the most general one that could be made ; we might assume that the specific inductive capacity of the strained body became difl'erent in different directions, So that the body would behave like a crystal. Dr. Kerr's experiments on the double refraction in liquids placed between the poles of a powerful electrical machine seem to point to this conclusion. Kirchhoff ^ has made similar assumptions to those of Korteweg and Lorberg on the effect of strain on the specific inductive capacity, and has arrived at similar equations ; in the second paper he applies these equations to some cases which Quincke investigated experimentally. ' V. Helmholtz, Wied. Ann., xiii. p. 385; WissenscJiaftl. Abh. vol. i. p. 298. ^ Korteweg, Wied. Ann., ix. p. 48 ; Lorberg, Wied. Ann., xxi. p. 300. ' Wied. Ann., xxiv. p. 52, 1885 ; Ibid., xxv. p. 601, 1885. 156 EEPOET— 1885. Second Report of the Committee, consisting of Professor Schuster (Secretary), Professor Balfour Stewart, Professor Stokes, Mr. Gr. Johnstone Stoney, Professor Sir H. E. Eoscoe, Captain Abney, mid Mr. Gr. J. Symons, appointed for the purpjose of considering the best methods of recording the direct intensity of Solar Radiation. The Committee, working on tlie lines of their last report, have given their attention to the best form of a self-recording actinometer, and have come to the following conclusions : — 1. It seems desirable to construct an instrument which would be a modification of Professor Stewart's actinometer adapted for self-registra- tion — the quantity to be observed being, not the rise of temperature of the inclosed thermometer after exposure for a given time, but the excess of its temperature when continuously exposed over the temperature of the envelope. 2. As the grant to the Committee will not admit of the purchase of a heliostat, it will no doubt be possible to procure the loan of such an instrument, and, by making by its means sufficiently numerous com- parisons of the instrument proposed by the Committee with an ordinary actinometer, to find whether the arrangement suggested by the Committee is likely to succeed in practice. The Committee would therefore confine their action for the present to the carrying out of such a series of comparisons. 3. The size of the instrument might be the same as that of Professor Stewart's actinometer. 4. The instrument should have a thick metallic enclosure, as in the actinometer above mentioned, and in this enclosure there should be inserted a thermometer to record its temperature. Great pains should therefore be taken to construct this enclosure so that its temperature shall be the same throughout. 5. The interior thermometer should be so constructed as to be readily susceptible of solar influences. It is proposed to make it of dark glass, of such kind as to be a good absorber, and to give it a flattened surface in the direction perpendicular to the light from the hole. 6. It seems desirable to concentrate the sun's light by means of a lens upon the interior thermometer, as in the ordinary instrument. For if there were no lens the hole would require to be large, and it would be more difficult to prevent the heat from the sky around the sun from interfering with the determination. Again, with a lens there would be great facility in adjusting the amount of heat to be received by employing a set of diaphragms. There are thus considerable advantages in a lens, and there does not appear to be any objection to its use. The Committee have not drawn their grant (201.). They suggest that they be reappointed, and that the unexpended sum of 20?. be again placed at their disposal. ON OPTICAL THEORIES. 157 Report on Optical Theories. By E. T. G-LAZEBROOK, M.A., F.R.S. Dk. Lloyd's well-known Report on Physical Optics was presented to the Association at its meeting in Dublin in 1834 — fifty-one years ago. Since that time the question of double refraction has been treated of very fully by Professor Stokes in the Report for 1862, but unfortunately he con- fined himself to that one branch of the subject. The years immediately succeeding that in which Dr. Lloyd's report was read were mai'ked by work of great importance, which has formed the basis for much that has since been done, and it is necessary, before writing of recent progress in the subject, to consider somewhat carefully the researches o£ Green, MacCullagh, Cauchy, and F. Neumann. This 1 propose to do, in as brief a manner as possible, for that part of the subject which is not included in Professor Stokes's report. I then propose to go on to the consideration of more modern work, treating sepa- rately (1) of the simple elastic solid theory, (2) of theories based on the mutual reactions of matter and ether, (3) of the electro-magnetic theory. PaKT I. — IXTRODUCTION. THE WORK OF MACCULLAGH, KEUMANy, GREEN, AND CAUCHY. Chapter I. — MacCullagh. § 1. Fresnel ' himself had developed a theory of reflexion and re- fraction, and had arrived at formulas giving the intensities of the reflected and refracted waves in terms of the incident. In obtaining these he relied on the two following principles : — The resolved parts of the displacements parallel to the face of inci- dence are the same in the two media. The total energy in the reflected and refracted waves is equal to that in the incident wave. He further supposed that the rigidity of the ether is the same in all transparent media, and hence that reflexion and refraction are produced by a change of density ; from this it follows that the refractive index of a medium is proportional to the square of the density of the ether in the medium. The direction of vibration is considered to be perpendicular to the plane of polarisation. According to this theory there is a discon- tinuity in the component of the vibration at right angles ^ to the surface. § 2. An elegant geometrical expression of the laws to which these principles lead was given by MacCullagh. He defines as the trans- versal of a ray the line of intersection of the wave front and the plane of polarisation ; the length of this line being proportional to the ' Fresnel, Ann. dc Chlm. et do Physique, t. xlvi. p. 225 ; (Eiivres completes, t. i. p. 767. ^ For a further consideration of this point see p. 186. 158 EEPOBT — 1885. amplitude of the vibration multiplied by tbe density of tlie medium. Then Fresnel's results may be expressed by the statement that the trans- versal of the incident ray is the resultant, in the mechanical sense of the word, of those of the reflected and refracted rays. This first suggestion of MacCullagh's was modified by reading some of Cauchy's work on double refraction, from which it appeared possible that the vibrations of polarised light might lie in the plane of polarisa- tion instead of at right angles to it. Adopting, then, this hypothesis, a transversal represents in addition the direction of vibration ; and if the further supposition is made that the ether is of the same density in all media, so that reflexion and refraction arise from variations in its rigidity and not in its density, expressions very nearly identical with Fresnel's can be found for the intensities of the reflected and refracted rays, while at the same time the principle of the continuity of the displacement normal to the surface is satisfied. § 3. These three principles — (1) The ether is of the same density in all media, (2) The displacement is the same on both sides of the surface of separation of the two media, (3) The energy of the incident wave is equal to that of the reflected and refracted waves — were applied by MacCullagh to the problem of reflexion and refrac- tion at the surface of a crystal, and the results of a first investigation were communicated to the meeting of the Association in 1834. The theory as there given was somewhat modified in consequence of a, paper by Seebeck in Poggendorif 's ' Annaleu,' and took its final form in a memoir read before the Irish Academy ' in January 1837. MacCuUao-h in this paper states his fundamental principles, not as based on mechanics, but merely as those which had led him to a solution, the results of which agree closely with the experiments of Seebeck and Brewster. The analysis of the problem is greatly simplified by the introduction of the idea of ' uniradial directions.' In a crystal, for any given direction of incidence, there are two posi- tions for the incident transversals, which give rise each to only one refracted ray — there are corresponding positions for the reflected trans- versals. These directions of the incident transversals are the uniradial directions. For a uniradial direction the incident, reflected, and refracted trans- versals lie in one plane, and the refracted transversal is the resultant of the other two. The transversal is normal to tlie plane containing the ray and the wave normal. The polar plane is defined as a jDlane through the trans- versal and parallel to the line joining the extremity of the ray to the point in which the wave normal meets the surface of wave slowness, here designated the ' index surface.' It is hence proved that for a uniradial direction the incident and reflected transversals lie in the polar plane of the refracted ray, and then the principles of equivalence of vibrations and of vis viva lead to equations to determine the relation between the azimuths of the trans- versals referred to the plane of incidence. ' lyiacCullagh, ' On the Laws of Crystalline Reflexion and Eefraction,' Januarv, 1837, Trans, of Royal Irish Academy, vol. xviii. ON OPTICAL THEORIES. 159 These give — tan 6 = cos (<p - f') tau 6' + si" Y tan x cos d' sin ((f) + f') (1) tan 0, = - cos (^ -t- d,') tan 8' + sm -»ja^nj^_ cos d' sin (^ — 0') with exactly similar formate for the other uniradial direction ; ft, 0;, and ti' are the azimuths of the transversals in the incident, reflected,'and re- fracted waves measured from the plane of incidence, and % tlie ano'Ie between the ray and the wave normal. In the general case the incident vibration is resolved into two in the uniradial directions, and each considered separately. When the two values of «,, found from these, are equal, the partial reflected transversals coincide ; the value of ^i at which this takes place is the deviation, and the angle of incidence the polarising angle. The theory is applied to Iceland spar, and agrees with experiments of Brewster and Seebeck. § 4. The same problem is considered by Neumann ' in a long paper read in 1835 before the Berlin Academy, and in a second memoir pub- lished separately in Berlin 2 in 1837, and the same results deduced from similar hypotheses. § 6. In 1839 MacCullagh ^ attempted to found his theory on a dyna- mical basis by finding an expression for the potential energy of the ether when strained by the passage of the waves of light, and applyino- to the expressions thus obtained Laplace's principle of virtual velocities.'^ This leads to a volume integral which holds throughout the space occupied by the medium, and a surface integral to be taken over the boundary. The surface integral taken in connection with the principle of the continuity of the displacement gives the conditions at the surface and these are shown to be identical with the conditions found in the previous paper. ^ Professor Stokes, in the Report on Double Refraction, has pointed out the error in the fundamental expression assumed by MacCullao-h for the energy, and this error of course affects the theory of reflexion. ^ Chapter II. — Geeen. § 1. The correct expression for the energy, and the correct laws of re- flexion and refraction on a strict elastic solid theory, had at the date of MacCullagh 's paper been given by George Green * in a memoir read before the Cambridge Philosophical Society in December 1837. The potential energy of the medium is shown to be a function U) ot tJie three principal elongations s„ s^, s^, and the three principal shearing -strains a, /3, y. ft' ,'^.^y''\"^^-'^^^Tetische Untersuchuug der Gesetze nach welchen das Licht an der Granze zweier vollkominenen durchsichtigen Medien reflectirt und gebrochen wird° dieInw'u•T;,^'^''■•.'^?^^^^^^^^' "^"^ Krystallfliichen bei der Reflexion und ttber ^i!.r^l l"^* "^""^ gewohnlichen und ungewohnlichen Strahls.' See also ' Vorlesuo^en fiber tWtische Optik,' von Dr. F. Neiimann, edited by Dr. E. Dorn. Leipzi' sfs «r,dP t'^r"'"^.^'^'^ Essay towards a Dynamical Theory of CrystaS Reflex 'on and Refraction,' Tram, of Royal Irish Academy, vol. xxi. ^enexion Geo. Green, ' On the Laws of Reflexion and Refraction of Light at the fommnn 160 KEPORT — 1885. This function is then expanded in the form ? = V>0 + </>i + '/>2 +• • • • 00, &c., being homogeneous functions of the orders 0, 1, 2 of the small quantities Sj, s^, &c. The equations of motion depend on '60, and so, (po being constant, it does not appear. If the medium in its equilibrium position is unstrained 01 vanishes also, and in general 02 contains twenty-one arbitrary coeffi- cients. 03 may be neglected compared with 02- If the medium be not initially free from strain, 0, will introduce six more coefficients, so that finally we find the most general form of for our purposes involves twenty-seven coefficients. • Green then supjDOses the medium to be symmetrical with regard to three rectangular planes, and obtains finally as the form for f, taking the case in which the medium is initially strained, the value — _20=2A*'-f2B*^-H2C 5' ^ civ dy az , ^T^ dv dvj , or\ <^" (^^y 1 OT? '^"^ ^'" dy dz dx dz dx dy + + G + L ydz dy J \dz dx) \dy dxj ^ ^ If the medium be initially unstrained A=B=C=0, while, further, if it be completely isotropic, G = H = I = 2N -f-R"! L = M = N j» . . . . (2) P = Q = R. J And introducing two new constants, A and B, n^ . fdn , dv . dw\^ — 202 = A -- + •— + -y- ^^ \dx dy dz ) . (dv dw , dw du du dv\ \ ^o\ \dy dz dz dx dx dy) J ■ For the difference between this and Cauchy's theory see Prof. Stokes's report. ON OPTICAL THEORIES. 161 According to Green's theory of double refraction, founded simply on the supposition that the displacements are in the wave front in a crystal, G = H := I = /i, say Q=/i-2M f The equations of motion are given by j^^Mjdz[p(piu ^-d<p\ =0 (4) (5) In treating of the problem of reflexion this integral is applied to the whole of the two media, and is transformed by partial integration into a volume integral, which may be written and a surface integral, which we may write \dy dz (X cu — Xj cmj) + dzdx(Jlv — Yylv{) + dx dy {7i Iw — Zj Iw^. These two integrals must vanish separately. Green's work as to the former, on which the propagation of light depends, has been considered by Professor Stokes. It leads to the three equations — ^^" /A -o\ ^ fd^*' , dv , div\ , Tj „ 9 ' df^ — (K — TV\ / -1- 4- ^ 4- R V7 2 dy \dx dy dzj d^io d /du dv div^ dz \dx dy dz , p— =(A-B)^J^^ + ^ + ^^) + Bv^^« (6) which form the basis of the whole theory of isotropic elastic solids, § 2. The latter integral equated to zero gives us the surface condi- tions ; for over the surface, according to Green, who treats the ether in the two media as two separate elastic solids always in contact with each other, we must have • . . (7) • • . (8) and hence «=Mi, t;=fi, w=-w^, X=Xi, Y=Ti, Z=Z,, These six equations determine the motion completely. Using Green's notation, and considering only the case of two homo- geneous media, let us take the plane x=0 as the separating surface. Then the surface conditions become 1885. i(=M^, V^Vi, W = lVi, M 162 REPORT — 1885. \dx dy dz J \dy dz J . Aiwi dvj . r?WiN _ 22 A7f'i , dw^ \ \dx dij dz J ' V% d7. J rdu dv\ _ -g I'dxi _^ dvi\ \dy dxj ' V dy dx J fdu div\ _ -o (dMi ,dw^\ \di "^Ite; '\dz^ dx J B B . (9) when a;=0. The problem now resolves itself into two cases. Let ns take the plane of incidence as the plane xy, and suppose that the vibrations in the incident wave are perpendicular to this, then — Case I. — Light polarised in the plane of incidence, and the conditions are T-) dw -r, dw] dx dx } (10) Now, we have seen that Fresnel originally assumed that the rigidity of the ether is the same in all media, and the density different. Green, adopting this view, puts B=Bi, A=Ai,* and the above formula lead him to results agreeing with those given by Fresnel's simple theory for this case, while, by making the angle of i-efraction imaginary, it is shown that the wave, when totally reflected, undergoes just the change of phase given by Fresnel. Case II. — Light polarised at right angles to the plane of incidence, the vibrations being therefore in that plane. Then i(; = t(;i=0, and the surface conditions are U = U-,, V = V, Z«, " \ dx dy) dy \ dx dy ) dy = -R, f'^'^i^.'^ll) -ry/du dv \dy dx, . (11) J ' V dy dx We have here four equations to determine two unknowns, viz. the inten- sities of the reflected and refracted rays, and it is clear, therefore, that two more quantities must come under consideration. Now, in the general case it follows from the equations of motion given above that two waves can traverse the medium. In the one of these the vibra- tions are transverse, and travel with the velocity \/B/p. This constitutes the lio-ht-wave. In the other the vibrations are longitudinal, and travel with the velocity^ A /p. In the case before us, then, reflexion gives rise to both these, and we have two reflected and two refracted waves. But experi- * The physical meaning of these constants and the relations implied by these conditions will be considered later, see p. 167. ON OPTICAL THEORIES. 163 ment tells us, id a bigli degree of approximation, that the whole of the energy of the incident light appears in the reflected and refracted light. "We are therefore forced to suppose not merely that the longitudinal wave does not affect our eyes as light, but also that it does not absorb any material part of the incident energy. This conclusion is confirmed when we recollect that on arriving at a second refracting surface this longi- tudinal wave would, if it existed, set up transverse vibrations which would be visible, so that on passing through a prism, for example, there would always be two emergent rays. Now, Green shows that very little energy will be absorbed by the longitudinal vibrations, provided that the ratio A/B be very small or very great ; and, further, that the condition of stability of the medium requires that A/B should be greater than 4/3. He therefore concludes that A/B is very great — practically infinite, or that the wave of longi- tudinal vibrations travels with a velocity enormously greater than that of light. The equations are then solved, assuming that B = Bj and A = Ai,* by the substitutions — eld) , d4'\ dz dij d^_d\li dy dx (12) The symbol represents the longitudinal or, as Sir Wm. Thomson has called it, the pressural wave, and \p the transverse or light wave. It is shown that by the reflexion a difference of phase is produced between the reflected and incident and the refracted and incident waves, and expressions are found for the intensities of the reflected and refracted waves in terms of that of the incident. According to these expressions, the mtensity of the reflected wave never vanishes, but reaches a minimum when f + <p'z= 90°. The minimum value of the ratio of the two intensi- ties will be for air and water about 1/151, while for a diamond or other substance of great refractive index it would be much greater still. § 3. This result, then, of the theory is in direct antagonism to the fact that light is very nearly completely polarised by reflexion from most transparent surfaces at the polarising angle, while the values found for the change of phase do not agree with the experiments of Jamin,' ^mcke, and others, and the theory as left by Green is certainly incorrect. We shall, however, return to this point later.^ Green does not apply his equations to the problem of crystalline reflexion, and, indeed, his theories of reflexion and of double refraction are entirely inconsistent, for the former supposes the ether to have the same rigidity in all bodies, while the latter attempts to explain double refrac- tion by making the rigidity of a crystal a function of the direction of the strain, * This last equation, as we shall see later, is not necessary. Jamin, Ann. de Chimie (3), t. xxix. p. 263 ; Quincke, ' Experimentelle optische ^ntersuchungen,' Pogg. Ann. See also Haughton, Phil. Mag. (i), vol. vi. p. 81. * See p. 192. ^ -^ ■/' t; M 2 164 EEPOKT — 1885. Chapter III. — Cauchy. § 1. Cauchy 's optical researches were being published about this same period, and a very full and interesting account of them, and of the work of other French authors, is given by M. de St. Venant in a paper to which I am greatly indebted for much valuable information.' Cauchy 's work on elastic solids began in 1822, and in 1829 he pre- sented to the Academy his first memoir on isotropic media. His more generally known memoir followed in 1830,^ containing his work on double refraction and the propagation of light in a crystal. An account of this is given in Professor Stokes's report in 1862. His first work on dispersion, which he explained (following a suggestion of Coriolis) by the addition of terms involving differential coefficients above the second, was published in 1830.^ The great memoir, ' Sur la dispersion de la lumicre,' in which he developed this principle, appeared between 1830 and 1836 ; ■* and in this same memoir he first considered the problem of reflexion and refraction, which led him to the idea of elliptic polarisation and a more general expression for the possible displacements of a molecule * in a plane wave. § 2. Further considerations on the subject of reflexion and refraction led him to conclude that, in order to obtain Fresnel's expressions for the intensities of the reflected and refracted rays in terms of that of the incident, it was necessary that not only the displacements, but their differential coefficients with respect to the normal to the surface of separation, should be continuous across that surface. This continuity had to be rendered compatible with the rest of his theory, in which the ether is considered as differing both in density and elasticity in different media.'* It is, however, quite inconsistent with the true surface con- ditions established by Green, Neumann, and MacCullagh on their various hypotheses — the conditions, namely, that the displacements and the stresses over the surface should be the same in the two media; and Cauchy, in con- sequence, was led to conclude that the method of Lagrange, by which the above conditions were first established, is inapplicable to questions of this kind.^ But, as St. Venant points out, these sui-face conditions do not in the least depend on Lagrange's method of virtual velocities, but on the fundamental elementary principles of mechanics, and can never be recon- ciled with Caucliy's theory of continuity so long as it is supposed that the rigidity of the ether varies from one body to another. § 3. In 1839 * Cauchy re-established his equations of motion for an isotropic medium, basing them on analytical considerations of symmetry. For a perfectly isotropic body he arrived at the equations — p^=(A-B)f + Bv2« . . . (13> dt'^ dx , „ dti , dv dw Ac, where ^ = Tx'^^j^^' ' De St. Venant, 'Sur les diverses mani^res de presenter la thSorie des ondes- lumineuses,' Ann. de Chimie (S. iv.), t. xxv. p. 335. " Cauchy, Exercices de Mathcmatiqncs, t. v. pp. 19-72. ' Cauchy, Bidletin de M. dc Fcrusmc, t. xv. p. 9. * Noum-aux Exercices de Mathimatiques. * C. It. t. 'vii. p. 867. » a R. t. viii. p. 37i ; t. x. p. 266. ' C. R. t. xxvii. p. 100 ; t. xvi. p. 1.54 ; t. xxviii. pp. 27, 60. • C. R. t. viii. p. 985; Exercices d'Anahjsc, t. i. p. 101. ON OPTICAL THEORIES. 165 already given by Green. ^ And in cases in whicli the axes can only be turned together aboat the origin, a third coefl&cient comes in, in the form of terms, such as p fdw dv \dy _dv\ dzj' In 1849 ^ Cauchy propounded the idea that the ether atoms in a body such as a crystal are disposed, as it were, in shells round the matter atoms in such a manner as to have different elastic properties at different points of the same shell ; the shells, however, are regulai'ly placed, and the properties of the ether repeat themselves at similar points in the different shells. It results from this that the constants in the equations of motion will be periodic functions of the equilibrium positions of the molecules, and for optical effects we hare to do with the average displacement over a small volume of the medium.^ The general equations established by Cauchy lead to a normal wave travelling with a velocity equal to \/A/p. According to his earlier theory, resting on the law of action between the molecules of ether, A and B are not independent, and it is possible by suitably choosing the law of force to make A vanish or even be negative. The theory * of reflexion and refraction led him to conclude that A was a small negative quantity, so that the normal disturbance ceases to be propagated as such. § 4. Canchy's work was continued by Briot,' starting from the equations of motion deduced from the mutual action between two par- ticles of ether, and the supposition suggested by Cauchy that the ether within a crystal is in a state of unequal strain. In treating of dispersion Briot points out that it cannot be explained in the manner originally suggested by Cauchy, for there is no reason why the terms in his differ- ential equations from which it arises should be insensible in a vacuum if they are sensible in ordinary transparent media. He therefore makes it depend on terms arising from a periodic distribution of the ether within material bodies, and shows that to obtain Cauchy's dispersion formula the law of action between the molecules must be as the inverse sixth power of the distance. In his memoir on reflexion and refraction, however, he adopts Cauchy's views as to the disappearance of the normal wave, and this is quite inconsistent with the above law, while the ether and matter mole- cules must attract each other with a force varying as the inverse square of the distance. § 5. The problem of reflexion and refraction for both isotropic and crystalline bodies is treated of in a memoir published in 1866-67,^ start- ing from Cauchy's principle of continuity, to which he gives an extended meaning in the second memoir. He at first supposes the vibrations in the crystal to be rigorously in the plane of the wave, and, adopting MacCuUagh's methods of the uniradial direction, arrives at his equations. The work is then extended to the general case in which the vibrations o^ ' See p. 161. ' a R. t. xxix. pp. 611, 644, 728, 762 ; t. xxx. p. 27. ' For the further development of this by M. SaiTau, see p. 174. * C. R. t. ix. pp. 677, 727, 76.5. On this point cf. Green's theory. See also Stokes's, Brit. Assoc. Report, 1862, and pp. 170-195. * Briot, Essais siir la theorie mathematiqiie de la lumiere. Paris, 1861. ' Liouville's Jouriial, t. xi. p. 305 ; t. xii. p. 185. 166 EEPOBT— 1885. are quasi-transversa], and it is shown how the simpler forms of the equations are modified by this. Thus, for the uniradial directions in the case in which the longitudinal disturbance is supposed to be strictly normal to the wave, if ^ is the angle between the ray and the wave normal, 6, 6', and 0, the azimuths of the planes of polarisation, measured from the plane of incidence, of the incident reflected and refracted waves, (p and f' the angles of incidence and refraction, and m a quantity depending on the angle between the plane of the wave and the direction of vibration, then — tan 6 = tan 0' cos (0 — (//) + -. — -~ —^ cos sin (</< -t- ?' ) , /■; /. . /\ '"' sin^ (/>' tan v tan 0, = tan 0' cos (^ + 0') — ^ ^ (14) cos W' sin ((^ — 9') These formulte agree with those of MacCullagh if we put m = 1. Chapter IV. — Elliptic Polarisation. Compaeison of Results, § 1. The peculiar phenomena presented by quartz had been explained by Airy in 1831 ^ on the assumption that the two waves were elliptically polarised. In 183G ^ MacCullagh made a further advance, and showed how the addition of certain terms to the diflFerential equations of motion would lead to the elliptic polarisation required by Airy's theory. The equations assumed by MacCullagh, for the existence of which he does not attempt to assign a mechanical reason, were — Ti^ ~ 7f-? Iff , Where A ^ a\ B = a" - {a" - 1"") sin^ 9, (15) a and h being constants, and the angle between the optic axis and the wave normal — the axis of z. The two waves resulting from these equations are shown to be elliptically polarised, while their velocity is given by the equation K-A)(i.^-B) = ^ . . . (16) X being the wave length. The rotation of the plane of polarisation produced by the passage of a plane polarised ray through a plate of crystal cut at right angles to the axis, and of unit thickness, is 'l-Jz'^Cja^X^. MacCullagh shows that the results of this hypothesis as to the form of the equations agree fairly with Airy's experiments, and that the agreement would be made somewhat more close by the hypothesis that C varies slightly with 0. ' Airy, ' On the Nature of tlie Two Eays produced by the Double Eefraction of Quartz,' Camh. Phil. Soc. Trans, vol. iv. pp. 70, 198. ^ MacCullagh, ' On the Laws of the Double Refraction of Quartz,' Irish Trans, vol. xvii. p. -IGl. ON OPTICAL THEOEIES. 167 § 2. Terms of a similar kind were first applied by Airy ' to explain the magnetic rotation of the plane of polarisation discovered by Faraday. Airy starts by calling attention to the fundamental difference between the rotation produced by quartz and that due to magnetic action. In quartz, sugar, etc., by reflecting the ray back along its original path the rotation is reversed, so that the ray emerges with its plane of polarisation unaltered, while in bodies under magnetic action the rotation is doubled by the same process. It is as if the former effect were due to a heliacal arrangement of the molecules, the latter to a continuous rotation of them round the lines of force. Airy shows that the effects produced can be accounted for by the introduction into the equation for u of terms involving odd differential coefficients of v with respect to the time, and he works out the case in which the equations are W ~~ dz^ dt cPv . d^v _ f>,dzi clr'~ d? dt . The two possible velocities for a wave of period r are given by Vi^ =■ — ■ , f -J = . (17) It is pointed out also that terms such as — r — or would also dz^dt dfi lead to the effect observed ; though they would differ in the law, express- ing the relation between the velocity and the wave length. Airy remarks that ' the equations are given, not as offering a mechanical explanation of the phenomena, but as showing that they may be ex- plained by equations, which equations appear such as might be intro- duced by some plausible mechanical assumption.' § 3. The attempt to estimate the relative value of the theories of reflexion and refraction just developed is rendered easier if we consider the physical meaning of the two constants involved. The importance of this has been continually insisted upon by Sir Wm. Thomson ^ in his numerous writings on the subject of elasticity, which have done so much to clear away difficulties and obscurities ; and though these writings belong to the later period of our subject, we shall consider here some of the results they lead to. To Green, Cauchy, and MacCullagh, A and B are constants, appearing m the most general form of the equations, and on which the rate of propa- gation of waves depends ; their connection with the other physical pro- perties of the solids is not considered. Now an isotropic 'elastic solid is one which possesses the power of opposing resistance (1) to change of shape, (2) to change of volume, and has in consequence only two prin- cipal moduluses of elasticity. ' -^iiTi 'On the Equations applying to Light under the Action of Magnetism,' PMl. Mag. (.S), vol. xxviii. p. 469. " See especially, Thomson, ' Elements of a Mathematical Theory of Elasticity,' Phil. Tram. 1856, p. 481 ; Thomson and Tait, A Treatise on Natural Philosophy, vol. i. ; Thomson, article ' Elasticity,' Encyclojitedia Britannica, ninth edition, 1880. 168 KBPOET — 1885. On fhe value of the one, the rigidity, n, in the notation of Thomson and Tait, depends the resistance which the body can oppose to a stress tending to produce distortion or change of shape without change of volume, and it is measured by the ratio of the shearing stress — or stress tending to produce distortion — to the strain or alteration of shape pro- duced. It can be shown that this is equal to the constant, B, of Green's theory. And the velocity of a wave of transverse displacement, since it does not produce changes in the volume of the body through which it passes, depends only on the ratio of the rigidity to the density. On the value of the other principal modulus depends the resistance which the body can ofier to compression or change of volume when sub- jected to a uniform hydrostatic pressure at all points of its surface. The compression produced is measured by the ratio of the change in volume to the original volume, and the modulus of compression, k, is the ratio of the stress to the compression it produces. It has been shown by Thomson that the relation between A and the principal moduluses is given by the equation A =: 7^ + f n, so that 1c, the modulus of compression, is equal to A — fB. The expression for the stresses arising from simple elongations e,f, g in the directions of the axes, and from simple shears a, /3, y round the axes, are found ; they are ^, = (h + in)e+ (lc-in)(f+g) = {k + |n)(e +/+ g)-2n(f + g) . fdu ,dv dw\ _ Q-D fdv clio\ \dx dy dzj \dy dzj^ etc., using Green's notation, and = na =Bf dz dy) ' etc., and from these Green's expression for the energy can be obtained. We may note that the velocity of propagation of the longitudinal waves ^/ A/p depends on both the modulus of compression and the rigidity. According to the mathematical theories of Navier, Poisson, Cauchy, and De St. Venant, there is a definite relation between n and h for all bodies given by the equation n =■ ^h or B ^ ^A. Stokes ' was the first to point out that this could not be true universally, and this conclusion has been confirmed by the experiments of Wertheim and Kirchhoff for various metals. Thus, on the assumption that the properties of the ether are those of an elastic solid, Cauchy's theory in its original form, independently of the consideration of his surface conditions, must be rejected. In his later theory, as we have said, he does admit the second constant A.^ But, we have seen that the existence of the two constants A and B implies that there will be two waves in the medium, while the absence of the wave of normal vibrations in light, combined with the conditions of stability, requires that A should be great compared with B, and this again requires that h, the modulus of compression, should be great compared with n, the * Stokes, ' On the Friction of Fluids in Motion and the Equilibrium and Motion of Elastic Solids,' Trans. Camh. Phil. Soc. 1845 ; Math. Papers, i. p. 75. 2 See pp. 164, etc. ON OPTICAL THEOEIES. 169 rigidity. Thus we are compelled to treat the ether as an elastic solid of very great — practically infinite — incompressibility. Now, the cubical dilatation produced by a given state of strain is measured by e +/+ g, or — + — + — , and the condition of incompressibility requires that this dx dy dz should be zero. It is not, however, admissible to omit the terms in e+f+g in the equations, for they occur with the constant A as a factor, and the physical condition that these terms should vanish implies also that A should be very large. To obtain the correct equations we must put / K -DN ^du , dv , dw\ ^^-^UJ.+ di,^'d^)==-^' and they then become 4>-| + Bv%. . . . (18) et cetera. § 4. MacCuUagh and Neumann omit the terras in p entirely from their equations, both within the medium and over the surface, and are led in consequence to erroneous results, though, as we shall see later, their theories (modified so as to include the terms) have been developed by Lord Rayleigh ' and Lorenz. Green, as we have seen, is perfectly con- sistent throughout ; but his final equations, unfortunately, are not con- firmed by experiment. If we assume the rigidity of the ether to be the same in the two media, it is not difficult to show that Cauchy's surface conditions are identical with those of Green, or, to be more accurate, that Green's correct equations expressing the continuity of the stress and of the displacement over the surface reduce to Cauchy's. Green obtains his surface condition from the value of a certain integral over the surface ; they may be obtained, perhaps more simply, from the equations of motion of an element dS of the surface ; for, taking the case when the plane x=0 is the bounding surface, let v be the thickness of the element, Nj, N/ the stresses on it parallel to the axis of x, then we have prdS'^^=(Ny-TS,')dS . . . (19) Hence, when v is indefinitely decreased, N,=Ni', with other similar equations. On Green's supposition that A^A,, B^Bj, these conditions for Case I. (vibrations normal to the plane of incidence) lead to div _dwi , " • • • . • • (^^) dx dx and for Case II. (vibrations in the plane of incidence) to du dui dv dvi 't • • (^U dx dx ^ dx dx' } which are Cauchy's conditions. The difi'erence between the two theories lies in their treatment of the waves of longitudinal displacement. > See p. 189. 170 REPORT— 1885. According to both Green and Cauchy they depend on a function 0, where ,p = ,p^e ""'■'' + "'■'■''"> .... (22) And in both theories a'2 + &2 = ^ (23) Green puts A/p very large, so that a'^ + h'^=0, and (j) = ei'-'^IK sin (hj + ct) + Lcos (hij + ct)} . . (24) while Cauchy, without any dynamical justification, writes A/^=— c^/P, k being a large quantity, so that A is a small negative quantity. Hence a'^ + b^= -P. The assumption of a negative value for A leads to the conclusion that the modulus of compression is negative — that is, that the medium is such that pressure causes it to expand and tension to contract, and this alone is fatal to the theory. § 5. We come, then, to the conclusion that the phenomena of reflexion and refraction cannot be explained, any more than the phenomena of double refraction, on a purely elastic solid theory involving a sudden change of properties on crossing the interface. Green's theory is the only possible consistent one, and it, in its original form, leads to results differing from experiment. Part II, — Modern Developments of the Elastic Solid Theory. We now come to the consideration of rather more modern investiga- tion on this subject. The limits of space will confine us to the theoretical work which has been done. The great experimental researches of Fizeau, Jamin, Quincke, Cornu, and others, will only be occasionally referred to. A complete account of these must be left for some future time. Chapter I. — General Properties op the Ether on the Elastic Solid Theory. The elastic solid theory of the propagation of light and double refrac- tion has been discussed in various papers by Haughton, Lame, St. Venant, Boussinesq, Von Lang, Sarran, Lorenz, Rankine, Loi'd Rayleigh, Kirch- hoff, and others. § 1 . Haughton considered the problem of the general equations of an elastic solid in a paper read before the Irish Academy in 1846, in which he adopts Cauchy's views as to the constitution of the medium. These views are modified in a second paper,' read in 1849, in which the general equations are formed, and the correct expression found for the potential energy. In this paper Haughton shows how to calculate the strain in any direction produced by a given elongation in the same direction. This strain is proved to be inversely proportional to the fourth power of the radius of a certain surface, called by Rankine the tasimonic surface. A form is found for the equation to the surface of wave slowness, which is said to reduce to MacCuUagh's if the vibi'ations be strictly transversal ; but, in making the reduction, the dilatation is equated to zero, its co- ' Haughton, ' On a Classification of Elastic Media and the Law of the Propaga- tion of Plane Waves through them,' Irish Trans, vol. xxii. p. 97. ON OPTICAL THEORIES. 171 efficient remaining a finite quantity, and in conseqnence the results are erroneous. § 2. Lame is the author of numerous papers, in the ' Comptes Rendus ' and elsewhere, on the propagation of waves througli an elastic medium, and his results are summed up in his ' Le9ons sur I'Elasticite.' '' The general form of the equations for the strains are shown to contain twelve constants, which become six if the dilatations be equated to zero, and three when planes of symmetry are taken for the co-ordinate planes. The equations of motion finally obtained may be written W~'^'di! \dy~~dx) ~" 'Lh\Iir~ d^J ' • '< ^' etc., which agree with MacCullagh's and with Green's if we omit the terras involving the dilatation. The arguments to be advanced against the theory are identical, then, with those which Professor Stokes has urged against MacCullagh's. § 3, St. Venant has written many most important papers on the subject of elasticity. He still adheres to Cauchy's theory and the form of the equations of an elastic solid deduced from the hypothesis of direct action between the molecules of the medium, and in his last great work on the subject, the annotated French edition of Clebsch's ' Elasticity,' states his reasons for so doing in §§ 11, 16. However, in the work he employs Green's expression for the energy, with the twenty-one co- efficients — ' Vu la controverse actuelle ou la majorite des avis est con- traire au notre.' § 4. In It paper printed in 1863 "^ he criticises Green's theory of double refraction, arguing that Green's conditions for the tranversality of the vibrations lead to isotropy. This conclusion is frequently repeated in St. Venant's ^ papers, and it will therefore be well to investigate the point somewhat closely. Let us suppose that we have a simple elongation e in a direction li, mj. 111, i^ ^ medium falfilling Green's conditions. Let I.2, mo, n^, I3, TO3, ^3 be the direction cosines of two lines at right angles in a plane normal to Z,, TOj, n^, and let us investigate the stresses N/, Ng', N3', T/, T2', T3' on the faces of an element normal to these directions. Then St. Venant's argument rests on the fact that N/ is independent of the direction of the elongation, while Ta'and T3' vanish, and that this would be the case in an isotropic medium. This last statement is of course true, but on Green's theory Na'. ^3' ^o depend on the direction, which they would not do in an isotropic medium, and T/ has a finite value, while for an isotropic medium it would vanish. The values for the stresses may be shown to be — - 1^2'= (iU-2(LZ32-|-MTO32 + ]^n32)}J N3'={yu-2(LZ2^-j-Mm22-i-N„,22)}.l , . (2) T/ = 2 {hlj3 + Mi».,m3 + Nnjng) e T2' = T3' = J Lame, Zegonit sur I'Elasticite. Paris : Gauthier Villars, 1866. ■^ St. Venant, 'Sur la distribution des elasticitSs autour de chaque point d'lm solide,' LiouviWs Journal, S. ii. t. viii. p. 257. 3 See especially De St. Venaiit, 'Theorie des ondes lumineuses,' Aim. de Cldm. S. IV. p. 22. 172 REPORT — 1885. For an isotropic solid we should have Nj' = N3' =: (yu — 2L) e and T/ = 0. Thus Green's medium in which the propagation of transverse waves is possible has properties which distinguish it fi'om an isotropic solid, for a simple elongation produces on any plane parallel to the direc- tion of the elongation a normal stress which depends on the position of the plane, while it also produces shearing stress about an axis parallel to the direction of the elongation ; and although the theory does not explain double refraction satisfactorily, yet it is not open to De St. Venant's criti- cisms on this point. § 5 In the same jDaper St. Venant proposes a modification of Cauchy's theory which leads to Fresnel's wave surface without any more conditions than are required by Green ; for, putting in Green's expression, AZ2 + Bm2 + 0^2 = X . . . . (3) I, VI, n being the direction cosines of the wave normal, the equation to ■determine the velocity becomes — {p V2 - X - G/2 - Hm2 - Iw2} [(p V2 - X)2 - (p V* -X) {(M + N)Z2 + (N + L)m2 + (L + M) n^} + MNZ^ + NLjn^ -j- LM«2] - {(H - L) (I - L) - (L + P)2} {GZ2 + Nto2 + M».2 + X - pV^} mhi" - {(I -M) (G - M) - (M-t- Q)2} (NZ2 + Hm2 + Ln^ + X - pY''}nH'^ - {(G - N) (H - N) - (N + R^2} {MP + hw? + In"^ + X - pV^} Vm'' + {(G - M) (H - N) (I - L) + (G - N) (H - L) (I - M) -2(L-|-P)(M + Q)(N + R)}Z2»i%2 = (4) And this will reduce to Fresnel's surface if A = B = C ; that is, if the equilibrium stresses are equal, and the four conditions (H-L)(I-L) = (L + P)2 X (I-M)(G-M) = (M + Q)2 (G - N) (H - N) = (N -h R)2 !" • (5) (G - M) (H _ N) (I - L) + (G - N) (H - L) (I - M) -2(L + P)(M-l-Q)(N + R)=0 are satisfied. These equations include those of Green's first theory, and are approxi- mately those which arise from what St. Venant calls an ellipsoidal distribution of elasticities. Under certain circumstances the tasinomic surface — which, it will be remembered, gives the tension in any direction produced by a simple elongation in that direction — reduces to an ellipsoid, and then the distribution of elastic constants is named by St. Venant ellipsoidal. This distribution is produced when an isotropic medium is unequally sti'ained in three perpendicular directions. The theory is interesting, and important as showing that Fresnel's wave surface can be deduced from the general elastic solid theory on other assumptions as regards the constants than those given by Green, and that the vibrations in this case are not necessarily in the wave front. There will, however, in this case be a quasi-normal wave, the velocity of which is given by the equation p72 _ X- GZ2 - Hm2 - I/i2 = ; ON OPTICAL THEOBIES. 173 and if Green's arguments as to the relative magnitude of the constants be still supposed to hold, the quasi-normal wave will disappear, and the vibrations will be very neai'ly indeed transversal. The theory, however, interesting as it is, does not enable us to overcome the difficulty of reconciling the theories of double refraction and reflexion so long as we adopt the view of Fresnel and Green, that the latter depends on difference of density, not of rigidity, in the two media. It is also open to the objection that if the medium be incompressible the displacements must be in the wave front, and we must get in this case Green's conditions, not the above ; while if the medium be not incompressible an appreciable amount of energy must exist in the form of longitudinal vibrations. § 6. The question of the propagation of waves through an isotropic medium, which is rendered anisotropic by the production of three elonga- tions, a, h, c, in three rectangular directions, has been studied by Bonssinesq.^ The elastic constants are taken to be linear functions of these permanent strains, and the number of constants involved in their expression is reduced from the considerations involved in the symmetry of the medium and the principle of the conservation of energy. The equations of motion may be written = (X + Va)'j? + (/z + pa)v dx ■u + «T {d'^u , T d^u , dy' dH \ dx 1 dx dy dz . (6). with the condition implied by the principle of the conservation of energy that \'= I', while if the normal stresses in the equilibrium condition vanish a = p. These may be deduced fi-om Green's equations by putting A=((7-p)a, B = ((T-p)&, C = ((r py, (7) with similar expressions for the other constants, A and fi are the two elastic constants of the nnstrained medium in the form in which they are written by Lame, v/X and ^/(X + fx) being the velocities of trans- verse and normal waves respectively, the density being taken as unity. _ _ It is thus shown that on the assumption that a, b, c are small quan- tities, such that their squares and products may be neglected, Fresnel's wave surface is given if either u =0 or o- = p. In fact, the condition «r = leads to Fresnel's surface without any assumption as to the value of a, h, c, for then the theory becomes identical with Green's second theory ; while if (T=zp we have either St. Tenant's ellipsoidal condition or his suggested modification of Cauchy, for to this degree of approximation the two theories are identical. Boussinesq, Liouville's Journal, S. ii. t. viii. 174 REPORT 1885. "We may conclude, then, that Fresnel's laws as to double refraction would hold in a medium strained in the manner Boussinesq considers, but the theory as a whole is liable to the same criticisms as have been made to Green's. Boussinesq is the author of another and different theory, which we shall consider later, and which gives a better explana- tion of the phenomena. § 7. This same problem has been dealt with by Professor C. Niven,' who has arrived at similar results without introducing considerations based ■on molecular reactions. § 8. The problem of double refraction has been treated in a different manner by M. Sarrau, following up the suggestions of Cauchy as to the nature of the ether in a crystal, aud his theory is developed in two papers in ' Liouville's Journal.' In these papers^ the density of the ether in a transparent medium is supposed to vary in a periodic manner from point to point. The ether is arranged in concentric shells of variable den- sity round each matter molecule, and its density, variable round each matter molecule, is the same at any one of a series of points situated similarly with regard to the matter molecules. The ether is periodically homogeneous, and the coefficients which occur in the elasticity equations are no longer constant, but are pei-iodic functions of the co-ordinates of the point whose displacement is being considered ; from these equations ^are deduced a series of others with constant coefficients, containing the ;average displacements of the ether in an element of volume. It is to •these average displacements that optical effects are supposed to be due. Cauchy ^ has indicated the path to be followed in deducing these auxiliary equations from the fundamental forms, and M. Sarrau arrives .at the following conclusion. If the fundamental equations be represented by df" \dx' dy' ihJ ' ' V ^=«(- • • ■) ?=H(. . . .). dt (8) "Where F, G, H are functions v?ith periodic coefficients of u, v, w and their differential coefficients, then the auxiliary equations will be — d^u = F' + G' + H' (Py_ ^ Y" + G" + H" h dt^ d^w ffi/// I n.'// I TT/'/ (9) ' C. Nlven, Quarterly Journal of Pure and Ajyplied Mathematics, No. .55, 1876. * Sarrau, C. R. vol. Ix. p. 1174. ' Sur la propagation et la polarisation de lalumifere •dans les cristaux,' Liouville's Journal, S. ii. t. xii. p. 1 ; t. xiii. p. 59. ' Cauchy, Comytes Jtendus, t. xxx. p. 17. ON OPTICAL THEORIES. 175 F', F", F'" being symbolic functions obtained by substituting integral functions of — , — -^ for the periodic coefficients of F, and similarly for dx chf dz 'J G', H'. The second memoir ' is devoted to the consideration o£ the problem on the supposition that the ether in a crystal is isotropic as regards its elasticity, and that the variations in density are all which we have to consider. Again following Cauchy, and treating the ether as a system of attracting and repelling points, Sarrau arrives at the equations <|-r=E(v> + r(v')|}. . . . (10) etc., where E and F are certain connected functions depending on the law of force, and d the dilatation. For free space — E(v2)=ev2, F(v2)=/, e and / being constants. For the ether in a crystal, omitting the consideration of dispersion, it is shown that it is probable that E and F have the same forms, only now e and / are periodic functions of the co-ordinates. If we denote djdx, djdij, d/dz, djdt by a, /j, y, a, respectively, then the equations in the crystal become, in conformity with the general rule, «r%= V2(F,« + F,v + F3M;) + (/,« +/;/3 +/37)9, etc., where F, G, H, etc., /, g, h, etc., denote now symbolic functions of «, /3, y. These general equations are simplified by the consideration of the various kinds of symmetry possible, and it is shown that in the case of ordinary biaxial crystals they reduce to dho ,.„2 , .• M^ ^'«_.„2 . (M _=^v^. + ^,-^, • • • • (11) d'^w , , ^ dd It is further assumed that f + fi ^= g + gi = h + h := 0. This, of course, is the condition that the velocity of the normal wave should be zero. These equations are solved by putting M=:Pe*('^+'"2'+»^-<"0, etc., and lead to ■ _P__ Q _ R ^ -(Fl+Qm + Rn), whence fl gm Tin y^—f <^^ — g 0)2 — A ■' ■ "' +7^=0- • • . (12) (li^—f w^ — g w^ — h ' Ziouville's Journa.!, Ser. ii. t. xiii. p. 69, 176 KEPOKT — 1885. Thus the wave surface is Fresnel's. The direction of vibration, the ray and the wave normal are shown to be in the same plane, but the direction of vibration is at right angles to the ray instead of to the wave normal. The assumed conditions / + j\ = 0, etc., form a serious objection to the theory as it stands, but on this point it is capable of modification. The vibrations, of course, are not strictly transversal within the crystal, but I am not aware of any experiments which prove that they must be so. Of course, if the medium be absolutely incompressible, the displacements must be in the wave front, and the theory fails ; but the condition of stability and the evanescence of the longitudinal wave require merely that the incompressibility should be very great compared with the rigidity, without being absolutely infinite. § 9. M. Sarrau has considered the peculiar phenomena presented by quartz, and shows how on his theory the terms assumed by MacCullagh will arise. For the crystalline symmetry of such a body, the equations are shown to take the form — dt^ •' \ dxj •" Kdij dzj d^v /„, dd\ . „2 /' <^^' , <^w^ d^w /„o dd\ , „2 /' t^^ I <i'"\ i (13) and it follows that two elliptically polarised waves can traverse the medium in any given direction. The velocities of these waves are given by -'=f7-|(:/-/)sinM ±l^{(sr_/)2sin4 + }^ (g.cos'^d + f.sm^O) x(g,cos^e-g,sm^d)^ . (14) fy and gf, are two constants which are probably very small, and, in that case, the squares of the principal velocities at right angles to the axis are/ and g, while the squares of the velocities parallel to the axis are given by If pi represent the ratio of the axes of the ellipse in the ordinary wave, P2 that in the extraordinary, then q^ cos^ fl — 9 1 sin^ ,-, r\ ^"'^-■^2Cos=^a + /,sin^0 • • • ^^^^ The major axis of the extraordinary ellipse is perpendicular to the prin- cipal plane, that of the ordinary ellipse is in the principal plane, while the two waves are polarised in opposite senses. § 10. De St. Venant ' criticises the theory in the following points, p being the only periodic variable, the equations, he argues, should be treated as if the ' St. Venant, ' Sur les diverses mani^res de presenter la theorie des ondes Inmi- neuses,' Ann. de Chim. (4), t. xxv. p. 335. ON OPTICAL THEOKIES. 177 periodic coefficient Tvas attached to the first term, p — —^ etc., and he states that the development of the equations p = . . . . leads to different results. Sarrau,' in reply, points out that this depends on the relative magnitudes of the quantities a, ft, y, a^, and the other parameters ; on making the same suppositions in the two cases the results, he shows, are identical. One may, however, start from the general equations of an elastic solid with two coefHcients, and, by supposing the coefficients to be periodic, arrive at the general equations already found. M. de St. Venant finds a difficulty in explaining dispersion, for in an isotropic medium the periodicity of the coefficients vanishes. This may be true, and yet the equations contain differential coefficients above the second. § 11. The theory advanced by Von Lang ^ might perhaps more strictly be considered under the next section : ' Theories based on the mutual action between matter and the ether.' The theory is, however, so slio-ht a modification of the ordinary elastic solid theory that it will be more convenient to deal with it now. Von Lang supposes that the displacements which come into the ordinary elastic solid theoiy are displacements of the ether relative to the molecules of the matter. He assumes that the ratio of the matter displacement to that of the ether is in general a function of the direction, but that for three directions we may write U=a2^t, V=i2y, W=c2m;, U, V, "W being displacements of matter, «, v, w of ether. He then forms the equations of motion, and, equating the velocity of the quasi-longitudinal wave to zero, arrives at Fresnel's wave surface. The theory cannot be regarded as having any real physical signification, for the elastic forces produced in the ether will depend on the real dis- placements of the ether particles, not on the displacements relatively to the matter, and the velocity of the normal wave cannot vanish, for if it does the medium becomes unstable. § 12. Von Lang ^ has also given a theory of circular polarisation, which consists in adding to the ordinary equations terms such as .-2 fdv _ dw\ \dz dyj' From this it follows that the velocity in a medium such as sugar is g^ven by 'Ztv a L being the wave length in air ; while in quartz 0,2 = a2 _ «l-_^8in20 ± 1 / I (^2 _ ,2)2 8in49 -j-^-^cos^flj . (16) Sarrau, ' Observations relatives k I'analyse faite par M. de St. Veuant,' Ann de Chim. (4), t. xxvii. p. 266. ^ Von Lang, ' Zur Theorie der Doppel-Brechnng,' Wied. Ann. t. clix. p. 168. ' Von Lang, ' Zur Theorie der Circular- Polarisation,' Pogg. A?m. t. cxix. p. 74. 1885. -^ 178 REPORT— 1885. Von Lang holds that the experimental law connecting the rotation and the wave length is h' Rotation ^h + -\- . . . . and this is given by the above expressions if a2 = m + -+ . . . . P = rh + ;' -f s L No reason is given for assuming the form 2^^^ •— — — - j rather than A that selected by MacCuUagh, o^f --^ — ^ ), which leads to the correct relation between the rotation and the wave length without any violent supposition as to the form of o^, such as is made by Von Lang ; and, though neither theory has any mechanical basis, this fact alone is suffi- cient to render MacCullagb's the more probable, while experiments on the size of the rings produced when convergent polarised light is trans- mitted through a plate of quartz cut at right angles to the axis agree rather better with MacCuUagh's form than with Von Lang's. § 13. Another theory of double refraction was developed by Lord Rayleigh ' in 1871. It had been suggested originally by Rankine,^ and Stokes in his British Association Report referred to it, and showed that in its original form it was untenable. The theory is also given by Boussinesq in a paper in ' Liouville's Journal,' ^ which will be considered in full under the next section. Lord Rayleigh points out the inconsistency already referred to be- tween the theories of double refraction and reflexion given by both Green and Cauchy, while, as we shall see when considering the polarisation phenomena accompanying the reflexion, difl"raction, and scattering of light, he believes that Neumann and MacCullagh, though consistent, were wrong throughout. He then remarks that the analogy of a solid moving in a fluid would suggest that the first effect of the matter mole- cules in a transparent body would be to alter the apparent density of the solid, and that conceivably this alteration might depend on the direction of vibration. He supposes that the statical properties of the ether are not altered by the presence of the matter, and the equations of motion may be written d'^U dp , -n^o I d^v dp , -D„o P — s = - + B V"^« ^vdf- dy d-lV dp , -r,„-y ^T/2 = 7 + ^^ "^ where p is written for A?, c being the dilatation. ' Hon. J. W. Strutt, ' On Double Kefraction,' Pkil. Mag. June 1871. ^ Kankine, Phil. 3Iag. June, 1851. ' See p. 215. (17) ON OPTICAL THEORIES. 179 Lord Rayleigh further assumes the medium to be absohitely incom- pressible, so that c is zero and A is infinitely large, p remaining finite ; this, of course, leads to the fourth equation — du , dv , dw n ^T + ^ + ^ = ^ .... (18) And from these equations the equation to the surface of wave slowness is shown to be — -1 ^-1 _-l a2 h^ c^ This, however, is not Fresnel's surface, and experiments of a very high ' degree of accuracy have shown that the wave surface in a •crystal is very approximately indeed Fresnel's surface, and of course this is fatal. But, as we shall see in the next section, according to all the theories yet proposed based on the mutual reaction between matter and •ether, the first and most important effect of the matter is to alter the apparent density of the ether in the way here supposed. The mutual 72 reaction, it can be shown, will introduce terms of the form Jc —^ into the dt^ equations, and k may conceivably depend on the direction. § 14. Equations of motion practically the same as Lord Rayleigh's are given by Boussinesq, Lommel, Ketteler, and Voigt, and the question arises. Are these equations incompatible with Fresnel's wave surface ? Lord Rayleigh has, of course, proved that they are if the equation du dv div ^ dx dy dz •expresses an absolutely necessary condition ; but it is not difficult to show that if, instead of the above equation, we put 1 ^w J. (^ 1 du „ a^ di b^ d^ '^ dz ~ ' ' ' ^ -^ then the wave surface will be Fresnel's, the direction of vibration will be normal to the ray, and will be in the plane containing the ray, the wave normal, and an axis of the section of the ellipsoid a^x"^ + I'^if + c^^^ = i by the wave front, and while the velocity of propagation will be inversely proportional to the length of this axis. Assuming equations of the same form as Lord Rayleigh's (17), we have to determine the pressural wave given by p —p^ti(ix+my+nz-\e) ^.j^g equation ■where ti = \Q^^Klx+my + ,iz-Yl), gtg_^ and this, on Lord Rayleigh's assumption of Ik + mu + wr = 0, reduces to Po = «B0oV^{^, + ^^ + ^y} . . . (21) • See Stokes, Proc. Roy. Soc. vol. sx. p. 44B ; Abria, Ann... de Chhnie; Glazebrook riitl. Trans. Pt. I. 1879 ; Kohlrausch, Wied. Ann. t. vi. p. 86 ; t. vii. p. 427. n2 180 REPORT — 1885. while, on the hypothesis suggested above, we should find po=-iBdQ{\l + lum + rn} .... (22) The theory as here modified would, it appears to me, agree in its results with all the experimental facts ; the main difiiculty lies in the assumption of equations of the form—. — =— ^ + V ^u for the medium when it is not ^ a''' at B ax strictly incompressible. The value of 2^ is generally A|-— + -=- +_— j, and the introduction of « is based on the supposition that - — | + -- ax ay dz is zero, and A infinite ; it is questionable if the substitution ought to be made, except in this case. § 15. Kirchhoff 's paper on double refraction ' was read before the Royal Academy of Berlin, and is contained in their ' Transactions ; ' its more important part deals with the problem of reflexion and refraction. So far as the double refraction is concerned, it does not differ in any important points from Neumann's theory. The medium is supposed to be incompressible, so that -{- — + — - vanishes, but the coefficient of this ax ay dz expression is treated as finite, and the terms involving it in the ex- pi'ession for the energy are omitted. The criticisms on Neumann's theory, contained in Professor Stokes's report, apply again here. Chapter II. — Dispersion of Light. In 1870 Ketteler ^ published a paper on dispersion, which forms the first of his important series on that subject. He commences with an account of Cauchy's theory and the various modifications which have been proposed. § 1. Redtenbacker ^ had considered the problem under the supposition that each matter molecule is surrounded by an ether shell, and obtained the formula J- = a+^+c\2 (23) \ being the wave length in the medium, and /x the refractive index. § 2. Christoffel,^ discussing Cauchy's formula, already mentioned,' viz. 1 ^ i ^ had shown that, while a and h may be considerable in value, the other constants decrease rapidly. This two-constant formula may be written — /^= .-, ■ /°^^.. r. • • . (24) I I v/0-^")V('-x')' ' Kirchhoff, Ahhandl. der Konigl. Ahid. zu Berlin, 1876. 2 Ketteler, ' On the Influence of Ponderable Molecules on the Dispersion of Light, and the Signification of the Constants of the Dispersion Formulae,' Poffff. Ann, t. cxl. p. 1. ^ Kedtenbacker, Bi/namiden-Si/stem, Mannheim, 1857. ■• ChristofEel, Fogg. Ann. t. csvii. * See p. 165. ON OPTICAL THEORIES. 181 Thus /uq and Xq are the refractive index and wave length for the shortest waves transmitted, and /itov/^the refractive index for the largest possible waves. § 3. The various theories are then compared with experiment, by Ketteler, and it is shown that the formula i,=KX>+A + g^.O .... (25) represents the results of the comparison most accurately. This formula was obtained by Briot, working on the same lines as Redtenbacker, but he supposes the coefficient K, which he shows depends on the direct action between matter and ether, to vanish. Van der WilHgen ' also called attention to the importance of the term in X^, but could not account for its existence. Ketteler, following Briot, then analyses the manner in which these various terms arise, and shows that the force on any vibrating ether particle may be written X2 < Displacement of particle > x{(, + /0(l-L)-^%f+^X^} This, of course, gives -l=A + g + KX2 (26) The term in g + h arises from the mutual reactions of the ether particles, supposed to be uniformly distributed. If the action of the matter be simply to produce a periodic variation in the density of the ether, the terms in L and M are introduced, while the term involving gi + h^ comes from a direct force expressed by mm^rf^{r) between the ether and matter particles wi and wij respectively. If we put rf^(r) = n/r", then the value of gi + 7i, is —^(n — 2)'Sim^fi/r"'^^. Briot supposes that the term KX^, to which this gives rise, is not requix-ed by the experimental results, and therefore puts w=2. Ketteler, however, shows that this term must be included. Holtzmann and C. Neumann had already insisted on the importance of retaining in the equations terms to express this direct action, and Neumann gives as the expression in an isotropic medium for the force arising from a displacement ti, Cu + C ^ + C" i^. But the theory of dispersion in its complete form requires that thu motion of the matter particles should also be included. This is treated of in the next section of the Report.^ A problem closely connected with dispersion is the relation between the refractive index and the density of a medium. This has been dealt with experimentally by various physicists, notably by Gladstone and Dale in England, and Ketteler in Germany. § 4. L. Lorenz ^ has recently developed the theory of the transmission ' Van der Willigen, Archives du Muue Teyler. - See p. 213, etc. ^ L. Lorenz, ' On the Refraction Constant,' WieA. Ann. t. xi. 182 KEPOBT— 188/5. of light through a medium consisting of a series of small spheres im- bedded in the ether. The velocity of light in the interspaces is the same as in free space, and the wave length is supposed to be great compared with the intei'molecular distances. It is assumed, then, that the disturb- ance u at any point may be written u= (t(Q + u<,)C + UiS, where the average values of 1*1 and «.> over the space containing some considerable number of molecules are zero, and C and S are written for the sine and cosine of kt — Ix — mij — nz — c. From this it follows that, if /z be the refrac- tive index and d the density, - ^ — _ is proportional to d.* The paper is followed by one by Lorenz and K. Prytz, giving the results of an elaborate series of observations which show a close agree- ment between this expression and experiment. Chapter III. — Aberration and Phenomena connected with the Motion OP THE Medium through which Light is being propagated. § 1. The aberration of light on the undulatory theory was accounted for by Fresnel • on the supposition that a moving body of refractive index fi carries with it a quantity of ether of density fi^ — l, the density in a vacuum being unity, while light is propagated through this ether, part of which is at rest and part mo^ang with a velocity v (that of the body), as if the whole were moving with the velocity (I— /i~')t;. The experiments of Fizeau^ on the displacement of the fringes of interference by a moving medium led to a result in close accordance with this theory, § 2. A more general and simpler proof than the one published by Fresnel of the fact that this leads to the ordinary laws of reflexion and refraction was given by Professor Stokes in 1846.^ In this paper Professor Stokes points out that the same result as to the velocity of light in the medium will be arrived at if we suppose the ether on entering the medium to be condensed, and on leaving it to be rarified, while the whole ether in the body travels with the velocity given above ; for, if we take two planes, one outside the other inside themedium^ each moving with the A^elocity v normal to itself, the quantity of ether which crosses the two planes per unit time will be the same, and hence, if V be the velocity of the ether in the medium, then we have, since the densities are 1 and fi^ respectively, and hence Y M^""-'- Moreover, this comes to the same thing as supposing the medium to be at rest, while the ether outside moves with a velocity v, and that inside with a velocity?;/^-. The direction of a ray is shown to be that in which the same jDortion of a wave moves, moving relatively to the medium, and is found by drawing from a given point a line of length V//i in a direction * Compare this with a similar paper by H. A. Lorenz, p. 255. ' Fresnel, Anvales de Chimie, t. ix. p. 57. - Fizeau, Annates de Chimie (3), t. Ivii. p. 385. ' Stokes, ' On Fresnel's Theory of the Aberration of Light,' Phil. Mag. vol. xxviii. p. 76; Afatheviatical Pajjcrs, vol. i. p. 141. ON OPTICAL THEOEIES. 183 normal to the wave, and from the extremity of this line a second of length v/f.i^ in the direction of motion of the ether; the ray is the line joinino- the first point to the extremity of this second line. The velocity of the ether is resolved into its components perpendicular and parallel to the reflecting sui'face, and the effect of each component is considered ; it is shown that rays are reflected and refracted according to the ordinary law of sines. § 3. But in a paper six months previously Professor Stokes ' had considered the problem in a much more general manner. He supposes that the earth and planets carry with them a portion of the ether sur- rounding them, so that close to their surfaces the ether is relatively at rest, while the velocity alters as we recede from the surfaces until, at no great distance, it is at rest in space. The direction in which a body is seen is normal to the waves which have reached the observer from the body, and the change in this apparent direction which arises from the motion of the ether is investigated. The axis of z is taken in the direction of the normal to the undisturbed wave, and a, f3, y are the angles which the normal to the actual wave makes with the axes ; u, v, w are the velocities of the ether at a point X, y, z at time t ; V the velocity of light. The equation to the wave is ^ = C + Vi + c, i being a small function of x, y and t. Then, by considering the displacement of the extremity of an element Ylt, drawn normal to the wave, it is shown that at time t + Zt the equa- tion is z = G + Yt + ^ + {lo + Y) dt, and hence we see that dZ_ , -w. At From this we find- If now IT 1 [dw 7 ,T TT 1 [dw , dio du dw dv dx dz dy dz so that udx + vdy + wdz is a complete differential, then «2 — "l = "vT- > P2 — P\ = w.,-zt, -; _ T _ ^'2 - ^1 and these equations, it is easily seen, imply the known law of aberration. In an additional note it is shown that if aj, /3i be the inclinations of a ray at any time to the axes, then fdiij dw\ -. \ ^^^=\jz-'d^Y' j,i f dv dw \ T. \az ay J (27) ' Stokes, 'On the Aberration of Light,' Phil. May. vol. xxvii. p. 9 (July, 1845) • Mathematical Pampers, vol. i. p. 134. ' 184 KEPOBT— 1.S85. So that, i{ vdx + vdy + ivclz be a comjDlete differential, Jctj and dj3i both vanish, and the path of the ray is a straight line. Thus, if the motion of the ether produced by the passage of the trans- parent medium through it have a velocity potential, all the phenomena of aberration will be such as are actually observed. The important ques- tion as to whether such a motion is probable in the ether is discussed in another paper. • § 4. Professor Stokes's views on the constitution of the ether are given in his well-known paper on fluid friction.^ He distinguishes there between the properties of rigidity and plasticity, pointing out that an elastic solid may under different external conditions become a viscous fluid, while the gradation between viscous and perfect fluids is quite regular. There seems, then, a probability that the property of rigidity will run to some extent through the whole series, becoming, in the case of fluids, masked by some other more important property. The mobility of a fluid is the limiting case of great plasticity ; but even a perfect fluid may admit of a finite, though extremely small, amount of constraint of the nature of shearing stress before being relieved from its state of strain by its mole- cules assuming new positions of equilibrium. A consideration of the length of a wave in light motion — about '00003 inches — renders it pro- bable that ' the relative displacement of the ether particles may be so small as not to reach, or even come near, the greatest relative displacement which could exist without the molecules of the medium assuming new positions of equilibrium.' These same views also tend to confirm the belief that for fluids, and among them the ether, the ratio of A to B (the elastic constants of the medium in Green's notation) will be extremely great. We are led, then, to conclude that, in considering the motion set up in the ether by a moving body such as the earth, we may treat the ether as an incompressible fluid, while, on the other hand, when dealing with the extremely small disturbance produced by the passage of a light-wave the rigidity of the ether may come into consideration, and the equations required will be those of an elastic solid. In the first case any tangential forces which may arise, if the fluidity be not perfect, will depend on the relative velocities of the parts of the fluid ; in the second case such tangential forces will depend on the relative displacements of those parts. In the paper in the ' Philosophical Magazine ' for 1846 Professor Stokes shows that it is probable that a velocity potential will exist unless the action of the air on the ether be such as to prevent it, and, further, that it is improbable that the air will so act. For suppose a sphere started from rest in such a medium, and then after a short interval stopped for a time, then started, and so on . The initial motion will have a velocity potential, and if the fluid were perfect this would continue, so that reducing the sphere to rest would stop the motion everywhere. But the motion with the velocity potential is shown to be unstable, and hence there is left in the neigh- bourhood of the sphere a small outstanding disturbance. This is carried ' Stokes, ' On the Constitution of tlie Luminiferous Ether viewed with reference to the Phenomenon of the Aberration of Liglit,' Phil. Mag. vol. xxix. p. 6 ; Math, aiid Phys. Papers, i. p. 15.3. * Stokes, ' On the Theories of the Internal Friction of Fluids in Motion, and the Equilibrium and Motion of Elastic Solids,' Trans. Cavib. Phil. Soc. vol. viii. p. 287; MatJi. and Phys. Papers, i. p. 75. ON OPTICAL THEORIES. 185 off with the velocity of light, which is about 10,000 times as great as that of the earth, so that at the end of the second interval the ether near the sphere is at rest again and the same effect is repeated. It seems, therefore, probable that there will be a tendency to set up a motion in the ether not having a velocity potential, but that the beginnings of such motion will be propagated away into space at a very great rate, and that the actual motion will satisfy the condition that udx + vdy + wdz is an exact differential. In a subsequent paper Professor Stokes gives the solution of the equations of motion of a sphere moving in a viscous fluid, and then proves that when the fluid becomes perfect the motion becomes unstable, so that udx+vdy + xodz is not a complete differential ; but if the tangential force depends, not on the relative velocities, but on the relative displace- ments of the molecules — that is, if for the beginnings of the variation from irrotational motion we must consider the rigidity of the ether (?".e , in our mathematics use the equations of an elastic solid) — then, as shown already, this nascent variation from irrotational motion will be propagated away by transverse vibrations, which, however, do not produce optical effects, either because they are too feeble or because they are discon- tinuous, or, if continuous, because their period falls outside that of the visible spectrum. Or, to put it slightly diffei-ently, if the fluid has any very slight rigidity, a given arrangement of its parts is not necessarily one of equi- librium. Suppose, then, the fluid displaced from rest by the sudden motion of the solid, and that after a short interval the solid is stopped, the velocity of the fluid will be reduced everywhere to zero, but the resulting configuration will not necessarily be one of equilibrium, and the motion arising from this slight strain will be set up. Thus, without making Fresnel's somewhat violent assumptions as to the relation between the ether within and without a transparent body, a perfectly reasonable and consistent account can be given of aberration depending only on the irrotational character of the motion induced by the moving body in the surrounding fluid. Unfortunately, as Professor Stokes points out, we have as yet no experiments competent to decide between the two, and he does not see how such experiments could be devised. § 5. Ketteler is the author of a long series of papers connected with the subject of aberration, which have appeared in Poggendorff's ' Annalen.' The last of these ' contains a summary of the results of the whole. The problem of reflexion and refraction at a moving surface is con- sidered, and it is shown that the intensities of the reflected and refracted rays will not be modified by the motion if the vibrations be at right angles to the plane of polarisation, as Fresnel supposed. § 6. The papers also deal with the problem of the emission of light from a moving source, and the principle first enunciated by Doppler,^ in consequence of which it follows that if the source and receptacle approach each other in time ^ by a space equal to n times the wave length in the medium between the two, then the receptacle receives in that time n more vibrations than it would if the two were relatively at rest ; and if this number be N, the apparent frequency is increased in the ratio N -)- «. ' Ketteler, ' Ueber den Einfluss der astronomischen Bewegungen auf die optisch n Erscheinungen,' Pt. VI., Pogg. A^m. t. cxlvii. ^ Doppler, Lasfarhige Licht der Dojjpel- Sterne. 1842. 186 EEPOBT— 1885. to N, or if V be the velocity of light, v that of the source towards the receptacle, in the ratio Y + v to V. This principle has been considered by other writers, among them Petzval, Von Ettingshausen, Klinkerfuess,' Van der Willigen,^ and Seccbi,^ and an interesting discussion of their work has been lately given by H. H. Turner, in a dissertation for a fellowship at Trinity College, Cambridge. Chapter IV. — Reflexion and Refraction. § 1. The various theories of reflexion and refraction advanced by Fresnel, Green, MacCullagh, Neumann, and Cauchy have been discussed by several writers, and attempts have been made to reconcile them with the experiments of Jamin, Quincke, and others. Jamin was the first to show that by reflexion at most transparent media plane polarised light becomes elliptically polarised, and that this elliptic polarisation is most marked when the angle of incidence does not difier much from tan -'//. Moreover, for some substances for which the refractive index is greater than 1-4 the phase of the component in the plane of incidence is re- tarded relatively to that at right angles to the plane, while if the index be less than 1'4 the reverse is the case. The original theories of Fresnel and MacCullagh do not in any way explain this phenomenon, and are therefore incomplete. § 2. Cornu'* has discussed the application of Fresnel's theory to crystals, and has suggested a means of explaining the apparent discontinuity of the displacement normal to the surface to which that theory leads. The explanation— which Professor Stokes has been in the habit of giving, independently of Corna, in his lectures at Cambridge — rests on the fact that the density of the ether is different in the two media. If, then, we take two planes in the two media parallel to the interface and at a small distance apart, the quantity of ether between the two planes remains the same ; hence, if u, u' be the displacements normal to the planes, and p, p' the densities, the equation of continuity gives pu= p'v! , and this is the condition assumed by Cornu in his papers. This con- dition, combined with those of the continuity of the displacement parallel to the surface, is consistent with the equation expressing the conservation of energy. The correctness of this condition depends on the view we take of the ether in the two contiguous media. If the two portions of ether be treated as two separate elastic solids in contact over a common surface, then over that surface the displacement must be the same in the two media ; but the equality of the displacement normal to the surface cannot extend beyond a very small distance within the medium, and in the dis- placement is included that which comes from the pressural wave, as well as that which produces light. During the motion, of course, the bounding surface of the two media does not remain plane, but is a curved surface,, the co-ordinates of any point on which at time i are w, -y + i/, w + z. ' Klinkerfuess, Astronomische Kachrichten, t. Ixv. p. 17, t. Isvi. p. 337. "^ Van der Willigen, Archives du Musee Teijler, t. iii. p. 306. ' Secchi, C. R. t. Ixxxii. p. 761, t. Ixsxiii. p. 117. * Cornu, ' Eecherches sur la reflexion crystalline,' Ann. de Chim. (4), t. xi. p. 283. ON OPTICAL THEOKIES. 187 The condition of no dilatation holds throughout both media, and the stresses over the surface are the same in the two. According to this view, a small portion of ether which belongs to one of the two media remains of unchanged density, and always forms part of the same medium. We may, however, consider the question somewhat differently, and look upon the ether in the two media as continuous, but of different densities on the two sides of the interface. A portion of ether belonging to the first medium may cross the interface and become part of the second, and in so doing its density is changed. There will thus be a thin sheet of ether lying over the interface in which rapid periodic changes of density are occurring. If, then, we consider the motion on the two sides of the sheet, we have for its determination the fact that the quantity of matter within the sheet is constant, and therefore that puz=zf)'u\ while the motion parallel to this sheet will ultimately be the same in the two media, and the energy in the reflected and refracted waves will be equal to that in the incident. But this condition pu=p'u' does not hold within the sheet where the variations of density are taking place, and where the effects of the pressural wave are appreciable. The motions denoted by m and u' are light-motions, exclusive of those which give rise solely to the pressural wave. Moreover, it is supposed that this layer of variable density is so' thin that the phase of the distui-bance may be treated as the same over its two bounding surfaces. It is further assumed that the above are the only conditions which hold at the surface, and these can be satisfied without supposing any change of phase to arise from the reflexion. As a fact, there are other conditions involved in the equality of the stresses over the surface, and to satisfy these it is necessary to suppose that when the vibrations are in the plane of incidence the phases of the incident reflected and refracted waves difier even at the surface. To assume Fresnel's conditions, as is done by Cornu, without change of phase is equivalent to supposing that this sheet of variable density is indefinitely thin when compared with the wave length of light. Green himself considered the effect of supposing tlie change in refractive index to take place in a gradual manner, replacing the refract- ing surface by a regular series of layers, of indices Hu fx^, etc., each of thickness t ; and proved that the effect of such a series would be to make the intensity of the reflected wave more nearly that given by Fresnel's tangent formula. The effects of supposing the change of properties from one medium to the other to be gradual was discussed by L. Lorenz in the year 1860. § 3. In his first paper • he supposes that Fresnel's formute express the result of a sudden transition, and investigates how they must be modified if the transition be gradual. The variable sheet is divided into a series of layers, each of constant density. A ray reflected at one of the interior layers will on emergence be retarded relatively to the ray reflected at the surface. Let I be the retardation of the ray reflected at a layer on which the angle of incidence is x, and let a, ft be the angles of incidence and emergence, then the disturbances in the reflected ray are shown to be : — ,r j-^; ^o^^'^^' ' On the Eeflexion of Light at the Bounding Surface of two Isotropic Media,' Pogg. A^m. t. cxi. p. 460. ^ 188 REPORT — 1885. (1) Light polarised in the plane of incidence — R = A s^" (" - /^) fcos kt + tan A sin ht\ . . (28) sin(a + /3)L J where . sin O cos a P/ o n i. ■ o -, , \dS , /-nrw tan A = -r-75 . - , ( COS'' p tan a; — sin- p cot j; )-dx- . (29) sm'' a — sm^ p}a\ J dx (2) Light polarised at right angles to the plane of incidence — R' = - A' ta n (a - ft ) V^^ ^^ + tan A ' sin kt\ . (30) tan (a + /5) L J 2a sin 2/3 f^r sin 2x _ sin 2ft~\dc -. .o-i >, a - sin2"2/3jl "^1^2/3 '^^^x \ dx ' ^^ where , , , sin 2fi tan A' =^2-0- 7^ Now -- is always small, hence A is small ; but for sin 2a = sin 2/3, ax or tan a = ft, tan A ' is infinite. Jamin's results as to positive and negative reflexion are shown to follow, and if it be assumed that the density is approximately proportional to/ii* — 1, the thickness of the variable sheet can be estimated, and is found to lie between ^L and -j-^^ of the wave length. In criticising this theory. Lord Rayleigh, in a paper we shall shortly consider, has pointed out that Fresnel's tangent formula does not express the result of sudden transition, and that Green's formula, which does, deviates from the truth on the other side. On the electro-magnetic theory, however, the tangent formula is strictly true, and Lorenz's investigations regain their interest. Another objection which Lord Rayleigh has made to the supposition of gradual transition, however, may be a serious one. It is that there should be some indication of colour in the light reflected near the polaris- ing angle, since it is to all intents and purposes a case of interference produced by a thin plate. It may, however, happen that the thickness of the plate is comparable with that of the black spot in Newton's rings, and so, though big enough to modify the quantity of light reflected, is too small to show colour. According to Newton, the thickness of the black spot in a soap film is about Jo of a wave length, while Reinold and Riicker have recently determined it as -g^^, and these fall within the limits required by Lorenz to explain the variations from Fresnel's tangent formula. In another paper ' the problem of reflexion at a surface across which the density varies gradually has been more fully considered by Lorenz, and the surface conditions on either side of the variable layer are deduced according to a strict elastic solid theory, and lead to similar conclusions. § 4. Cauchy gave the results of his theory of reflexion and refraction without the calculations which were supplied by Briot * in France, and Beer ^ and Eisenlohr '' in Germany. ' L. Lorenz, Poffg. Ann. t. cxiv. p. 238. '^ Briot, Liom-iUe's Journal, t. xi. p. 305 ; t. xii. p. 185. ' Beer, Fogg. Ann. t. xci. and xcii. * Eisenlohr, Fogg. Ann. t. civ. p. 346. ON OPTICAL THEORIES. 189 An account of the various theories is also given iu papers by Lord Rayleigb,' with a careful criticism and comparison of them all. In the first part of this paper Lord Rayleigh discusses fully the difference between the theories of Green and MacCullagh, and develops completely the consequences of the latter, taking into account the full effect of the pressural wave. This had been done first by Lorenz in the paper already referred to, and he showed that the results to which MacCuUagh's theory leads are totally inconsistent with experiment. Lord Rayleigh points out that the fundamental assumptions of Green and Fresnel amount to assuming an identity between the statical pro- perties of the two media, while the dynamical pi-operties depending on variation of density are different ; while, moreover, as we have seen already, Cauchy's surface conditions, founded on the principle of the continuity of the displacements and their differential coefficients with reference to the normal, though erroneous if we suppose the rigidity of the ether different in the two media, become identical with Green's if we adopt his fundamental hypothesis. The real difference between Green and Cauchy lies in their respective treatments of the pressural waves. The true surface conditions lead to the folio wins: results : — Let I, T], i^ be the displacements, n the rigidity, m the second coefficient, such that m + n is the A of Green's papers, and D the density, while g^ = (m + n) jD, y- = ?i/D for the one medium. Let a; = be the bounding surface, and let the axis of z be parallel to the front of the waves. And suppose/, F, and/i to represent the incident reflected and refracted waves, while f and ((>' are the angles of incidence and refraction. Then, for vibrations normal to the plane of incidence — tan f' n'\ F' tan (p n (32) f tan (p' i tan <i> 1 and this becomes : — Case I. n = n' (Green, Fresnel, Cauchy) — F^ _ sin (f - f) f 8in(f + ^) • • • • ^'i^) Case II D = D' (MacCullagh, Neumann)— F_ tan((^^-0) / tan (f + ^) • • • • ^''*^ Now, Jamin, Quincke, and others have shown that this latter formula is not strictly true, and hence at this point the evidence is already in favour of Fresnel's hypothesis. Turning now to the case of the vibrations in the plane of incidence, put. dx dij _ d^_d'^ dy dx ' J. W. Strutt, ' On the Reflexion of Light from Transparent Matter,' Phil. Mag. August 1871 ; ' On the Reflexion and Refraction of Light by Intensely Opaque- Matter,' Phil. Maj. May, 1872 o j j f"^ (35) 190 REPORT — 1885. Then ^ refers to tlie light wave and $ to the pressural wave ; let *' refer to the incident wave, *" to the reflected, ^, to the refracted, so that Tlr __ \p'gHa.T + l!i + cO r ijf//gt(-ax + 6i/ + ct) etc. Then the surface conditions become in general, if we put ^/ ^ y^U _ X, ^' - ^" = Y. i(«> + a)!) =*i - X 6(* — <I>i) = aY — a,^i 4.{m(a'2 + i^) - ^nb^} + ^nabY =<I)i {)«'(ai'2 + ^2) _ 2n'b''} + 2n'a,b^i . . (36) n{b''^i- a^X + i-&(«Y - «,^,)} = «' {^^X - a, 24', + ^•Z;(«Y - a,^,)} • • (37) MacCullagh, in his original work, neglects the pressural waves en- tirely, and pats $ = <t, = 0, dei'iving his result (Fresnel's sine formula) from equation (35). These results are inconsistent with (36) and (37), and therefore wrong. To obtain the correct solution we must remember that m is infinitely great, while a'^ + h^ is vanishingly small, and m(a'^ + b^) = Dc^. This is what has been done by Green, and applied by Lorenz and Lord Rayleigh to MacCullagh's theory. [Cauchy puts o.'^ + 6^ = —k"^. We shall consider the consequences of this shortly.] Hence (36) becomes D* - D'*i = -^(/i - n') — ' -. , \ ' (o8) c^ l ^ I Cask I. n = n' (Green). Then W-Ji tan (<p - <!>') f 1 + M' tan" (<p + <!>') ) * .gg. tan (<!> + (l>')\l + M2 tan* (f - ff,')) ' ' ^ ■> W and R being the amplitudes of the reflected and refracted waves, and 2 "I M eaual to ^- , while the diSerence of phase between the incident ^ 1^^ + 1 and refracted waves is e where cot e = L cot (<}>- (p>) . . . . (40) while between the reflected and refracted waves it is e', where cot e' = ^ cot (r/, +i>') . . . . (41) Case II. D = D' (MacCullagh's corrected theory). The equations are very complicated and lead, when the difference in the rigidities is very small, to two polarising angles of 22^° and Q'7^° respectively, results which are thus utterly at variance with experiments. Cauchy's theory leads to results the same in form as Green's, if we substitute — £ sin for M, e being a certain small constant. The solution is contained in the above equations if we tabe a'2 + b^= - l\ a,'2 + b-'=- t,^ ON OPTICAL THEORIES. 191 and put 27r/l 1 N T{k-kJ = -' • ■ . . (42) In Eisenlohr's account of Cauchy's work it is assumed at first that the normal waves travel with the same velocity as the transverse, and then the solution is modified by putting for X^^, \", the wave lengths of the normal waves, the values — l,,l/ — 1 and — Z'V — 1. This modifies tpii and ^", the angles of refraction and reflexion of the normal waves, so that their sines become imaginary, while cos ^^^ is real and negative, cos 0" real and positive. A difierence of phase is thus produced, determined by the following •equations : — tan e = p tan (^ — 0'), where and tan e'=^ tan (^ + f'), V = m."viii — l' Jamin's results show that^ is very small ; hence we may write where u is small, and then 2m sin (f> ^ ~ tVTt^ + sin^ 0) • • • . (43) Cauchy puts p = e sin f, when e is a small constant. Hence we must suppose that t is great compared with f. Lorenz and Lord Rayleigh have both pointed out the serious obiec- }^^ *'° «*" "'^'^^ *° ^^^ *^®°^y ^° *^^s fo^"^- The equation to determine * is d^ df '^W medium will be essentially unstable. Moreover, if Z; be a constant, e varies inversely as X, and chromatic effects , near the polarising angle should be much more marked than they are I 1 have, however, given an account of Eisenlohr's paper mainly because ot another suggestion he makes, which renders it very nearly identical with Green s. He suggests that the normal or preesural waves mav ' vanish by a sort of total reflexion, their velocity being very great com , pared with that of the transverse waves.' So that we have X , and X" very large instead of imaginary, and from this he finds _ \,^ - X"^ ^ X ^ + \"2 ("^^ This vanishing by a sort of total reflexion is exactly Green's theory, for 192 REPORT — 1885. if x' be the angle of refraction for a normal wave produced by a trans- verse wave incident at an angle <j>, then, with the notation of Lord Ray- leigh's paper, 71 sin^ x = ™ sin^ ^, and hence x is iniaginary unless (p is less than sin"'(n/?u). That is to say, if wt be infinitely large, the effects of the pressural wave are entirely confined to the surface, and, indeed, for this total reflexion, if we may so call it, of the pressural wave to take place, it is practically not necessary for the ratio of n to m to b© zero. If, for example, n/iu = 1/100, there will be total reflexion if f is greater than 0° 85', and for so small an angle of incidence as this the component of the vibration normal to the surface on which the pressural wave depends would be too small to produce a measurable efiect on the transmitted light. If we put \^JX" = f.iQ, then jJq is the refractive index of the medium for the normal vibrations, and we have for ^j p-':^^ (^5> Ho ' + 1 Now, it was shown, first by Haughton,' and then by Kurz, that the expressions (39-41) agree with experiment very closely if M or p be treated as a constant to be determined by experiment, and if we suppose p to have the form just given, then for sulphuret of arsenic, for which fi = 2-454, according to Jamin, ^Iq = TOSS. Green, going further into the mechanism of the motion, has shown, however, that on a strict elastic sohd theory we must have \,J\" = \/\' and fJo^h'- The last conclusion Eisenlohr calls ' durchaus unhaltbar,' and in this he is right if he means, that it does not agree with experiment, but wrong if he means that there is a flaw in Green's theory. The suggestion that ^ and /iq may be diff'erent is due to Haughton,^ but the reasons he has assigned for it have been shown by Eisenlohr to be invalid. Lord Rayleigh has suggested others which have great weight, and the importance of which will be more clearly seen when we come to consider some recent theories based on the mutual reaction between matter and the ether. The large quan- tities m and m' are, in Lord Rayleigh's paper, eliminated from the equa- tions by means of the relations viia'^ + h"") =Dc2, D and D' being the densities of the ether in the two media. Now, in the pressural wave we are only concerned with a layer of ether close to the bounding surface, and Lord Rayleigh's suggestion is that, although the transverse vibrations are affected nearly in the same way as if the transition were instantaneous, it may not be so for the surface waves, and that therefore we may put D/D' =yuo^ where /uq is less than fj. There are, I think, even stronger reasons for supposing /.iq and ^ to be difierent to be derived from the theory I have already referred to, which will be developed later. Thus the papers of Lord Rayleigh, Lorenz, and Eisenlohr show, con- clusively, that Neumann and MacCullagh's theory is inadmissible, and that Green's strict elastic solid theory, when slightly modified in a per- ' Haughton, Phil. 3/aff. (S. 4), vol. vi. p. 81 ; Kurz, Pog/;. Ann. t. cviii. 2 Haughton, Phil. Mag. (S. 4), vol.vi. p. 81 ; Eisenlohr, Pugg. Ann. t. civ p. 3t6. ON OPTICAL THEOEIES. 193 fecfcly reasonable way, leads to results agreeing very closely with experi- ment, while Canchy's method of treating the pressural wave requires an unstable condition in the ether. In another paper Lord Rayleigh ^ considers the problem of reflexion at the confines of a medium of variable density. The incidence is supposed to be normal, and in, the particular problem solved completely, the density is supposed to vary as the inverse square of the distance from a fixed plane parallel to the surface. This variable medium extends between the two planes x = x^^, a; = a'2, and the density is constant on the other sides of these planes, and it is shown that if the thickness of the variable layer is not very different from the difference in the wave lengths in the two, then, for the case in which the two media are air and glass, the reflexion will be excessively small. § 5. The paper by KirchhoS"- in which the problem of reflexion and refraction is considered has been already referred to. The theory there given is, in its results, nearly the same as those of Neumann and MacCullagh. The ether is not treated strictly as incompressible, though it is supposed that only transverse waves are propagated, and therefore that the equation du dv dw /N dx d)j dz is satisfied without the coefficient A becoming very large. These trans- verse waves falling on the interface of the two media would tend to set up longitudinal vibi-ations. Some surface action, however, is supposed to go on over the interface, the result of which is to quench these vibrations and the condition that this surface action should involve neither loss nor gain if energy is formed. This, with the three equations implied in the continuity of the displacement, makes four conditions from which the intensities and planes of polarisation of the reflected and refracted waves can be found. The theory differs from MacCullagh's merely in recognising the possibility of the existence of the normal waves, and then accounting for their absence by means of some unknown surface action. It is not a strict elastic solid theory, nor does it attempt to explain of what nature the surface forces are which quench the normal waves. The formulas to which it leads are identical with MacCullagh's,' and do not offer any explanation of the change of phase observed by Jamin. It can hardly be looked upon, therefore, as a satisfactory explanation of the phenomena, nor can we regard Kirchhoff's principle, as the fundamental hypothesis is called by various German'* writers, as one which may replace the true surfece conditions of an elastic solid. Chapter V. — Metallic Reflexion. § 1. Various experimenters — and among them Brewster, MacCullagh, Briot, Airy, Neumann, De Senarmont, Jamin, Quincke, Wernicke, and Conroy — have investigated the optical efl'ects produced by metallic re- ' Lord Eayleigh, Proceedings of London Math. Soc. vol. xi. No. 159. ' Kirchhoff, Aih. der Konigl. Akad. zu Berlin, 1876 ' See Glazebrook, ' On the Keflexion and Refraction of Light,' Proc. Camh. Phil Soc. vol. iii. p. ,329. * See Ketteler, Voigt, etc. 1885. o 194 KEPORX— 1885. flexions. They have shown that, in general, plane polarised light becomes elliptically polarised by such reflexion, and have measured the difference in phase between the components polarised in and perpendicular to the plane of incidence and the ratio of the intensities of these two vibrations. MacCullagh ' was the first to attempt to express the laws of this elliptic polarisation mathematically. He supposes that in the case in question the angle of refraction becomes imaginary, so that we have sin , , sin / , . . \ in rf)':= Ll cos Y + i sm X ), m \ J J, cos 0/ / , ■ • /\ cos d)'= ;i( cosv' + ismx ). He then substitutes these expressions in the values given by Fresnel's theory for the amplitude of the reflected ray, which he shews may be written in the form a+fe v' — i. Thus the intensity of this ray will be represented by a^ + V', and the difference of phase between the incident and reflected rays will depend on tan ~^b/a ; a and b are functions of w, in', x, and x', and these quantities are connected by the equation sin'^^' + 008^^0' ^1, which leads to two con- ditions, giving m' and x' in terms of vi and x- The final formulae are : — (1) Light polarised in the plane of incidence. p = D' + cos'' - 2D cos <p cos (x-xO (4,q) D^ + cos'^ + 2D cos cos (x— x') t^n24=^^^^^^^pO. . . . (47) X COS'' (j)—D^ (2) Light polarised perpendicular to the plane of incidence. T/2 _ ''"'* cos'' + D^ — 2Dm^ cos cos (y + xQ fAQ\ 7n* cos^ <p + D"^ + 2D»i2 cos f cos (x + x') tan2/- = -^P^\""^t'^"^^t^^^ . . (49) Where D'* = m'' + sin"* — 2m^ sin* f cos 2x and D'' sin 2 (x— x') = '"^^ ^™ ^X } • . (50) These formute are simplified in the case of metals from the considera- tion of the fact that the proportion of light reflected at normal incidence is nearly unity. It follows from this that m is very large and x' very small, so that we may put sin x' = 0, cos x' = 1 i^ ^^^c equations, and hence m' = cos /cos 0', And for Case I. — jj m' + m'"^ — 2mm' cos x ^ m"^ + m'"^ + 2invm' cos x , 2:rS 2inm' sin x \ m'^ — m^ ) (51) ' MacCullagh, Pruc. Irish Acad. vol. i. pp. 2, 159 ; vol. ii. 376 ; Trans. Irish Acad. 1 xxviii. Pt. I. ON OPTICAL THEORIES. 195 and Case II. — j,2 1 + TO^W'* — 2«lMi.' COS X 1 + m?rnl^ + 2min' cos v ., o , • \ ■ ■ (52) , ct o' zmm sin v tan 2;r - = - ^ § 2. Cauchy ' has also given equations founded on his principle of con- tinuity and the assumption of a peculiar form for the refracted ray which agree closely with those just established. His complete theory was never published by himself, and was first given by Eisenlohr. It has been further developed and criticised in some important points by Lord Bayleigh. Eisenlohr ^ takes for the displacement in a metal at a dis- — (p— ;•) tance r from a source of light the expression e ^' ' where X' is a com- plex quantity connected with A, the wave length in air, by the equation X = X' Re'«. Hence, using d and 8' to denote the angles of incidence and refraction, we have sin = Re'"^ sin 6' . . . . (53) The surface conditions of the continuity of the displacement and of the stresses become, as v^e have seen, identical with Cauchy's conditions of continuity of motion in the case in which the rigidity of the ether is the same in the two media, and the expressions for the intensity and change of phase for light polarised in the plane of incidence are most «asily obtained by transforming Fresnel's sine formula, which is strictly true. To effect the transformation put c» cos 2u = 1- cos 2a sin^ d\ C2 sin 2u ___ sin 2a sin2 d (93) m- a IP Then the intensity in the reflected wave is P = tan (/• - ^tt) .... (54) where cot/= cos (m + a) sin 2tan-ip— V while d, the change of phace, is given by tan d = sin (a + u) tan 2tan-i f^°lf\ ^ ^ (55) These values agree with those given by MacCullagh if we put R = m, a= - X, ' Cauchy, C. B. t. ii. p. 427 ; t. yiii. pp. 553, 658 ; t. ix. p. 727 ; t. xxvi. p. 86. Ziouville's JomttmI, t. vii. p. 338. * Eisenlohr, Poffj. Ann. t. civ. p. 368. 02 196 EEPOET — 1885. and therefore c sec = m', u = x' \ C56> For Hglit polarised at right angles to the plane of incidence, Eisenlohr proceeds by transforming Fresnel's tangent formula in a similar manner, and finds , „ ^- I'2 = tan (g-i^) ' • • • (57) where cot g = cos (a — u) sin 2tan-' ( ^ J . . (58) and the change of phase is given by tan d' = sin (a — u) tan 2tan"'— — '■ — -, . . (59) ^ ' K. cos Hence in the general case the ratio of the amplitudes of the two reflected components is tan /3 where cos 2/3 = cos (a + «) sin 2tan-M -^— — -^ J . . (60) and the difference of phase is given by tan (d' - d) = sin (a + u) tan 2tan-' ^_^_— ^ j . (61) These last equations depend on Fresnel's tangent formula, and this we know is not strictly true for transparent bodies. It is hardly probable, therefore, that the final equations for the difference of phase and the ratio of the amplitudes can be accepted as representing accurately the phenomena, and, in fact, Cauchy's theory as here developed isno great advance on MacCuUagh's original expressions, with which it agrees throughout. In this theory the expression for the disturbance in the metal IS e Ae -i ''^'""^ sin — (rR cos a - ct). k Hence the velocity of wave propagation is c/R cos a, as against c in air, and R cos a may be called the refractive index of the metal, while R sin a measures the co-efiicient of absorption. Now Jamin, Quincke, and others have measured the quantities d — d' and /3 of the formulas above, and from these Eisenlohr, in the paper already quoted, has calculated the values of R and o. He finds that for silver a = 83°. This result Lord Rayleigh has made the basis of a serious criticism on the whole theory. Lord Rayleigh ' endeavours to attach a physical meaning to the con- stants in these formula?, and in so doing starts from equations taken to represent the motion in the medium. Thus, for light polarised in the plane of incidence he assumes ' dt^ dt Vdx* di/J ' Hon. J. W. Strutt, ' On the Reflexion and Refraction of Light by intcnbel3r Opaque Matter,' PMl. Mag. May, 3 872. ON OPTICAL THEORIES. 197 with the solutions for the two media, / _- ^'g i(ax+b)j+vt) a. |^"e i(-ax+by+vl). (63) ^ __ ^ g i{a,x+bij+vl)\ J ^ ' where a = — ^ cos 0, 6 =-— sin e, ^; = — — , \ A. A being the angle of incidence. If we put y^ = n/D, y^i = n/D,, we get from the differential equations — <±i;=.y'ri-i^)=,\s^j. . . (64) a2 ^ j2 ^^2 y^ D^^y From this we get sin 6' = - sin 9, and hence /x is the quantity which F we have denoted by Re'". Hence We'^^ = '^~Jl - i^). . . (65) yi^\ D^vJ Thus R2 cos 2a is positive, and R^ sin 2a is negative, so that 2a lies between and — ^tt and tan 2a = hlB^v. Again, in the expression for the refracted wave we have a^ = [ja when 6 is zero, and hence we find that the real part of /i is positive, the imaginary part negative, so that finally a lies between and — ^tt. This result is contradicted by Eisen- lohr's value for silver, in accordance with which a = 83°, from which it follows that the real part of /x^ is negative, and this Lord Rayleigh says is tantamount to assuming the medium to be unstable. Eisenlohr ' has repHed to this that the objection is really one to the form of equation assumed by Lord Rayleigh, and that according to other theories (e.ij. Helmholtz on anomalous dispersion 2) real negative values of /x^ are con- templated. With this reply we may in a sense agree. Loi'd Rayleigh'a objection is a valid one, however, against the supposition that the peculiar effects of metallic reflexion may be explained by the introduction of terms such as in the differential equations of an elastic solid ether, and forms an insuperable argument against the attempt to account for the effects on a purely elastic solid theory. When, however, we come to consider the theories depending on the mutual reaction of the ether and maiiter, we shall see that under certain circumstances the relation between the periods of the ether and matter molecules may be such as to give a negative value to fi^, and thus render possible Eisenlohr's value for a. The general value for a^ for any angle of incidence caay be shown to be given by «! = "^Rc < cos (u + a) + L sin (« + a) > . . (66) < ' Eisenlohr, ' On the Keflexion of Light from Metals,' Wi^d. Ann. t. i. 2 See p. 220. 198 EEPORT — 1885. c and ?( being defined by the equations of page 195, so that tbe expres- sion for the refracted wave is ^^g?^p-Rcsm(« + a) sin— JRracos (u + a) + ysind + Yt\, where, it must be remembered, x is measured in the negative direction. Thus the coefficient of absorption is — Resin (u + a). According to the experiments of Jamin and Quincke, the refractive index: R cos a for metal varies between ^ and i. § 3. Wernicke,' however, deduced, from some experiments of his own, values lying between 3 and 4. Wernicke's experiments, however, were made by measuring the light transmitted at various angles of incidence by thin films of metal, and assuming that the light absorbed by a thick- ness d may be expressed by fc/i''"^'^^', while the refractive index ft is given by sinf^/sinfl'. Eisenlohr, in the paper already quoted, shows that the quantity calculated by Wernicke is really {R^ + sin^y}^, and that his experiments confirm Jamin's and Quincke's. In the second paper quoted Wernicke suggests, as the complete equa- tions of motion, the form .+Zh^ = (A-B)f- + Bs^''^ + Zk't(v''-^) . . (67} dt'" \ Jdx dtf^y J and other equations might be suggested which would give for the dis- turbance in the metal due to a point source expressions of the form t.---_27r A£~^''sin fbr — vt\ Chapter VI. — Diffeaction and the Scatteking of Light by Small Particles. § 1. The principle first enunciated by Huygens, and applied so trium- phantly by Fresnel to the phenomena of diffraction, which consists in breaking up a wave front into elementary portions, calculating the effect of each in disturbing a distant point, and then finding the total dis- turbance at that point by simply summing the effects due to each ele- ment of the wave front, is a direct consequence of the fact that the disturbances and velocities are so small that their squares and higher powers may be neglected. The differential equations found for the motion are linear, and the complete solution is the simple sum of all the individual solutions. Again, it is fairly clear that the disturbance pro- duced at any point by an element of a wave front will vary as the area of the element and the reciprocal of the distance between it and the point answered ; but it is not so clear how the effect is related to the angles which the line joining the element and the point make with the wave normal and the direction of vibration respectively. In Fresnel's theory of diffraction the consideration of effects produced • Wernicke, ' On the Keflexion of Light from Metals,' Pogg.Ann. t. clix. and clx. ON OPTICAL THEORIES. 199 by tlie vaxiation of these angles is omitted, and that, too, with perfect justice, for lie is only concerned with the effects in the neighbourhood of the normal to the primary wave, and the dimensions of the diffracting aperture ai'e small compared with the distance between it and the point at which the effects are considered, so that the change in either of these angles over the whole area of the diffracting area is small. Again, it is clear that the effect will be a circular function of r—vt, r being the distance between the element and the point at which the dis- turbance is sought, and v the velocity of propagation ; but the simple theory does not indicate the relation between the phase of this circular function and that of the function representing the disturbance in the original wave. § 2. Both these questions received their complete and final answer in the year 1849 from Professor Stokes.' We will quote a few words from the introduction to his paper : ' TJ^e object of the first part of the following paper is to determine on purely dynamical principles the law of disturb- ance in a secondary wave, and that not merely in the neighbourhood of the normal to the primary wave, but in all directions. The occurrence of the reciprocal of the radius in the coefficient, the acceleration of a quarter of an undulation in the phase, and the absolute value of the coefficient in the neighbourhood of the normal will thus appear as parti- cular results of the general problem.' The equations assumed for the motion. are those of an elastic solid in the form given by Green — Jdx etc., where dx dy dz (68) In the preliminary analysis the important general theorem involved in the equations is proved. It is then shown that the solution may be written S = ?i 4- £2 where and ^ _ '^ = etc ay ax dx dy dz d^ _dj]2 dy dx dx dy dz 'Stokes, 'On the Dynamical Theory of Diffraction,' Trans. Camb. Phil. vol. ix. p. 1 ; Math, and Phys. Papers, vol. ii. p. 243. (70) (71) (72) Soc. 200 EEPOKT — 1885. and that hence ^'="Mlr~^'°'^"^'^'^4l[, 1- (yw'" - z^")dv (73) It is proved that ? and w', at", w'" satisfy the equation — . = a^ V ''t d iO 7 9 _, 9 dt^ (74) . (75) and hence, hy Poisson's solution, where /and F are the initial values of I and dljdt respectively. If, then, the values of o and dljdt, w and dujjdt be given initially everywhere, the last equation, with the similar one for w, enable us to find S and w at any moment throughout the space considered, and then the equation (73) give us ^, ??, and C- In solving the equations for c, w, it is clear that if we first find the part of the solution due to the initial velocity, the part due to the initial displacement may be obtained by substituting in the solution for the initial velocity the initial displacement, and then differentiating with regard to the time ; and this proposition is proved generally for a system in which the forces depend only on the configuration of the system, and which is executing small vibrations about an equilibrium position. The integrals are then modified by suitable transformations. For L we have £,= -—, where ii'= dx 47r dv. Thus — 4<Tr\h is the potential of matter distributed throughout space with density S, and finally it is shown that ^ = f 47r (uqX + VqIj + Wqz) ~ (raf) . (76) where Uq, Vq, Wq ^^e the initial values of the velocities at the point x', y', z', at which dv is an element of volume, r the distance between x', y', z' and X, y, z, the point at which ^ is to be found. From this ^i can be found,- and in a similar manner So- The terms ir Vu <^[ arise from a wave of dilatation which is in general set up by any arbitrary displacement, and which travels through the medium with velocity a. If the initial disturb- ance be such that Cq = dcQJdt = everywhere, then this wave will not be formed. The terms ''2) Vij ^2 arise from a wave of distortion which ti'averses the medium with velocity h. If a disturbance be produced at a point O, and last there for a time r, then the motion at a point P, at a distance r from 0, will not commence until after an interval t, where t = r/a, P will be disturbed by a wave of dilatation lasting for an interval r ; it will be disturbed by the wave of distortion after a time rjh, and this disturbance will last for an interval t. ON OPTICAL THEORIES. 201 The general integral is then applied to two cases, which must be care- fully distinguished from each other. In the first case, suppose that a periodic force acting parallel to a fixed direction acts throughout a given element of volume in the medium. Let the plane of xz contain the fixed direction, and let the axis of a; make an angle a with it. Let D be the density, and T the volume of the element, and let (DT)-\/'(Orf^ be the velocity communicated to it in time dt. Then r cos n ,( r \ . cos a fi^ 47rD = sin a .f , r \ sin a f* ^=4 (77) Now, we have seen that in the ether the ratio ajb is probably very large, hence the first term in £, on which the normal vibrations depend, is pro- bably very small compared with the first term in C- The molecules of an incandescent body may be looked upon, at least very approximately, as centres of disturbing forces, and the above equations show us how it is that from such centres transverse vibrations only are propagated. If the ether be absolutely incompressible, so that a/b is infinite, then longitudinal vibration would be impossible. Suppose, now, the first term in 4 omitted, and pnt/(i) = c sin 27rit/X, Then for the most important term we have — y c sin a . 2 "(fc^-r) . . . (78) and the first term in I is of the order Xjirr compared with the leading term in i^. Hence, except at distances from the source which are com- parable with the wave length, the terms in I may be neglected, and the motion is strictly transverse. This solution applies to the case of an element of volume vibrating in any given manner and emitting light into the surrounding space. Every- thing is symmetrical around the direction of vibration of the element of volume. It does not apply, as has been supposed by some writers, to the problem of diffraction ; for in this case we have a train of waves being propagated through an aperture, and producing disturbance in the medium beyond. Let us suppose the aperture to be plane, and that plane waves are bemg propagated through it in the direction of its normal; take this for the axis of x, the plane of the aperture being x = 0, and the axis of z the direction of vibration. Let Oj be a point in the aperture, and consider the disturbance propagated in a small interval of time r, across an element c^S, at Oi. This disturbance occupies a film of thick- ness It, and consists of a displacement f{ht') and a velocity hf'{ht'). Thus, for a point O, at a distance r from O^, and at a time t, given by i = t' + r/h, the initial disturbance is the above displacement and velocity extending over a volume brdS about ; and if I, m, n are the direction 202 REPORT 1885. cosines of Oi 0, measured from Oj, then the values of I, rj, Z depending on the initial velocity are — mnds (79) while the values depending on the initial displacement are- Pnds i" = - 1," = - r = KI 47rr Imnds ffit-A ' (80) From this it follows that the vibration at O, arising from that at 0,, lies in the plane through OiO and the axis of z, and is perpendicular to the radius OjO ; and if (j> be the angle between the axis of z and the line OiO, that between OiO and the wave normal, the value of this dis- placement is — ' ^ . . (81) !: = ^ fl + cos o") sin ff fu-A Hence if f(bt) = c sin — bt, ^ = f^/'l + cos e\ sin f cos — fbt-A . . (82) and the total efEecfc at will be found by integrating this over the whole wave front. We have thus found the complete expression for the law of disturb- ance in the secondary wave, and can see in what way it involves and (ji, and how its phase is related to that of the disturbance over the primary wave. The theory of diffraction given by Fresnel, and applied by him to points in the neighbourhood of the principal wave normal, is thus fully justified, since for such points 6 is small, and cos d therefore approxi- mately unity, while ^ is nearly constant. The expression shows that an addition of a quarter period must be made to the phase ; but this will not affect the form of the diffraction pattern obtained. But the results of the investigation are of even more importance in their bearing on the relation between the position of the plane of polari- sation and the direction of vibration of plane polarised light. For con- sider a ray diffracted in a direction making an angle d with the incident wave normal, and let the plane containing the incident and diffracted ray be called the plane of diffraction, and let the directions of vibration ON OPTICAL THEORIES. 203 in the incident and diffracted rays make angles a,-, a,; with the normal to the plane of diffraction. Then the diffracted ray and the two directions of vibrations lie in the same plane, and the directions of vibrations are normal to the respective rays. Thus, if we form a spherical triangle by drawing lines from the centre of a sphere, pai-allel to the normal to the plane of diffraction and to the two directions of vibrations, since the direction of vibration in the diffracted wave is the projection on that wave of the direction of vibration in the incident wave, we have cos d = tan ftj cot a^ . . . . (83)' Now, let -cr and a be the azimuths of the planes of polarisation of the incident and diffracted Hght, measured from a plane normal to the plane of diffraction. Then, on Fresnel's assumption that the direction of vibra- tion is normal to the plane of polarisation, we have •=^ = 2 " "=2+""^' and tan a = sec 6 tan w ; while on MacCuUagh's hypothesis 'B7 = a,, a = uj, and tan a = cos 6 tan to- ... . (84) These two formulae can be tested by experiment, and afford a means, therefore, of deciding between the two theories of reflexion, and of deter- mining the question whether reflexion be due to a change of density or to a change of rigidity in the ether ; for the values of a corresponding to a series of values of -ro- can be observed for any given angle of difiraction, and if the values of w be taken at equidistant intervals, the values of a, and therefore the positions of the plane of polarisation of the diffracted light, will not be equidistant, but will on the first hypothesis be crowded towards the plane of diffraction, while on the second they will be crowded away from that plane. Professor Stokes was the first to carry out a series of observations of this nature ; he employed a grating ruled on glass at the rate of 1,300 lines to the inch, and the results of his experiments are decisive in favour of Fresnel's hypothesis. The experiments are troublesome, and the com- parison of the results with theory is complicated by the fact that the refraction through the glass plate on which the grating is ruled also produces a change in the position of the plane of polarisation. The amount of this change is the same on the two theories, and tends to- produce a crowding of the planes of polarisation away from the plane of diffraction, an effect opposite to that produced by diffraction on Fresnel's theory. Moreover, we may suppose that, when the ruled face of the grating^ is towards the incident light, either the diffraction takes place in air so that the wave enters the glass obliquely, or that the diffraction takes place in the glass after the light has entered the first surface normally, while when the ruled surface is away from the incident light the diffrac- tion may take place in air after passing normally through the glass, or in the glass so that the light after passing normally through the first sur- face emerges obliquely. '204 EEPOET — 1885. In any case we shall have tan a = m tan •ar , . . . . (85) where in is a function of the angle of diffraction and the refractive index, which can be calculated on either of the above hypotheses. The results were reduced by plotting from the experiments a curve with log m as ordinates and 0, the angle of diffraction, as abscissae. The curves given by the two theories on either of the above assumptions as to the relation between diffraction and refraction were also drawn, and a comparison of the two results ' leaves no reasonable doubt that the experiments are decisive in favour of Fresnel's hypothesis, if the theory be considered as well founded.' And, moreover, the comparison shows us that we must suppose the diffraction to take place before the refraction. Thus, when the grooved face is towards the incident light we must sup- pose the wave to be broken up in the air and then to be obliquely refracted through the glass, while when the grooved face is away from the light the wave must be treated as if it were diffracted in the glass and then obliquely refracted out, and Professor Stokes shows that it is a friori more probable from physical reasons that this is what takes place. § 3. In the results of the experiments a certain amount of irregularity is pi'oduced by the want of symmetry of the grooves of the grating, and Holtzmann,' who in 1856 repeated Stokes's experiments, failed to obtain consistent results with glass gratings, and had recourse in consequence to a Schwerd's lamp-black grating ; with this he obtained results more in accordance with the theory of Neumann and MacCullagh than with that of Fresnel. Holtzmann thought that Stokes had neglected to consider the effect of the longitudinal waves, ' and to this neglect he attributes the error of Mr. Stokes ; ' and Eisenlohr,^ who * had not read the great paper of Prof. Stokes,' attributes to him the same neglect, and endeavours to give a theoretical account of the question from Cauchy's standpoint. Of course both these authors were quite wrong in their estimate of Stokes's work, and Lorenz ^ showed, from some decisive experiments of his own, that Holtzmann's results were due to an error of his method. Lorenz gave a fresh demonstration of Stokes's theorem, and arrived at the same results. Lorenz appears to consider his method as more general than that of Stokes, but this is due to a misconception on his part. The results of his experiments agree with Fresnel's theory. § 4. The matter has since been experimentally investigated by Quincke,'* who showed that the method of forming the grooves on the grating was of the utmost importance, and whose experiments led to no decisive results, and moi"e recently by Frohlich.* Frohlich investigated the polarisation of the light reflected from a glass grating, but did not compare his results with theory. A few experiments of the same kind were made by Stokes in 1852, but he also omitted the comparison with theory. ' Holtzmann, Pogg. An?i. t. xcix. p. 446. 2 Eisenlohr, Pogg. Ann. t. civ. p. 3.S7. ' L. Lorenz, Pogg. Ann. t. cxi. p. 315. ■• Quincke, ' Experimentelle optische Untersuchungen,' Pogg. Anii. t. cxlix. p. 73. * Frohlich, Wiedemann, t. i. ON OPTICAL THEORIES. 205 Rethy ' developed a theory whicli covers Frohlich's experiments, and arrived at a formula with which they agree closely, but his fundamental principles are at fault. In his solution Rethy adopts a method given by Kirchhoff to find the effects of a given source of light. The equations to be solved are, if we neglect the terms involving dilatation, etc., with the condition Take ^^=v^vV du dv diu dx dy dz «& = ^- sm 27r I - - vj, + 2 I . . . (86) Then $ and its differential coeliicients satisfy the equations of motion,, and we require to find such solutions as will satisfy the equation of continuity. Rethy takes as solutions — da> • . (87) I. and d<t> d<t> '' = dy' ''=-dx' ^ = ^ • • II. u =- rf2<& d^^ d2$ tZ^d. ~ dxdy' " —~ dydz' "^ — dx" '^ ly"^ . (88) The distance r, of course, is measured from a point on the grating to the point at which the motion is being considered. Now each of these expressions of course represents the solution due to some arbitrary motion set up somehow over the grating. In Case I. the motion is a periodic twist of each element about the axis of 2, while in Case II. it is an oscillation parallel to that axis. But Rethy does not show how this motion is to be set up, nor whether it can represent the effect of a train of plane waves falhng on the grating and there diffracted ; and a little consideration shows that it cannot, for, according to the ordinary assumed properties of the ether, we cannot get the wave of twist only without linear displacement ; the second solution corresponds to that due to the action of a periodic force at the origin generatino- a certain amount of momentum, and not to the complete effect of a train of waves. If we compare it with Stokes's solution, we see that it is that part which arises from the effects of the velocity propagated across the element, and omits the part due to the displacement. Stokes's solution applies to the case in which energy is being propagated by waves passing across the orifice into the medium beyond, and depends on the direction of motion of these main waves. Rethy's solutio4i is that which arises from a centre of vibration situated on the surface, kept in motion by some extei-nal force and sending out waves in all directions into the medium. Still, we can arrive at a formula of the same nature as that given by Rethy, and which does agree with Frohlich's experiments, by means of a simple extension of Stokes's principles. This consists in supposing that ' ESthy, Wied. Ann. t. xi. p. 504. 206 REPOBT — 1885. the incident waves set np vibrations over the surface parallel to a fixed direction, and that these vibrations lie in the same plane as the incident vibrations, while these vibrations set up others in the diifracted waves which lie in the same plane as those over the surface, and are everywhere normal to the diffracted rays. Then, if eo be the angle between the incident wave normal and the distui'bance over the surface, ^o a-^id the azimuths of the planes of polarisation on Fresnel's hypothesis measured from the plane of incidence in the incident and diffracted waves, and c the angle of diffraction, it can be shown that ' cos <po tan f = sin 2 cot Cq + cos S sin (po . . (89) This expression is given by Rethy, and agrees closely with the results of Frohlich's experiments which were made with two gratings — the one of 19' 76 lines to a millimetre, the other of 162 lines to a millimetre. The value of eo depends on the angle of incidence when this vanishes, so that the vibrations in the incident wave are parallel to the surface . Sq — 90°, and the above formula becomes identical with Stokes's. In comparing the two it must be remembered that the azimuths of the planes of polarisation are measured, in Stokes's expression, from the normal to the plane of incidence, while in Rethy 's they are measured from the plane of incidence. A careful series of experiments by Cornu'-^ also lead to the conclusion that the vibrations are normal to the plane of polarisation. This con- ■ elusion coincides with that arrived at by Lord Rayleigh and Lorenz from considerations based on the phenomena of reflexion and refraction, and is further strengthened by the phenomena of polarisation produced when light is scattered by a series of small particles. § 5. Before considering this, reference must be made to a paper by Professor Rowland,^ of Baltimore, on the subject. This paper will be more completely discussed when we come to the electro-magnetic theory, to which it more properly belongs. Professor Rowland, however, con- siders that he has discovered an error in Stokes's work, in that according to it ' when a wave is broken up at an orifice the rotation is left discon- tinuous by Stokes's solution.' It is not quite clear, however, how this criticism is intended to apply ; for the rotation in the main wave is -completely determined when the displacement is known. Now, Professor Stokes has shown that when the orifice is of finite size the aggi-egate disturbance at any point due to all the elements of the orifice, as found by his formula, is the same as if the wave had not been broken up. The rotation, therefore, as given by this formula is also the same. Again, the rotation is propagated according to the same laws as the transverse disturbance, and hence the elementary rotation due to a given element of a wave propagated in a given direction is related to the direction and to the total rotation of the element in the same way as the elementary displacement propagated in that direction is related to the Actual displacement. Thus, if the displacements over the wave be ^ = 0, r, = 0, i: = c sin^^ {It-xX • See GlazebroQk, Proc. Camh. Phil. Soc. vol. v. p. 254. ' Cornu, C. R. ' Rowland, ' On Spherical Waves of Light,' PMl. Ma^. June, 1884. the rotations are ON OPTICAL THEORIES. 20^ 0, — c COS ^(bt—x), 0; A. A and the elementary rotation to which this gives rise is W2= — T-r <^^S (1 + ^°^ ^) s^^ 4' sin ^ (ht — r), A / A ■>l> being the angle between the axis of y and the radius vector r. This elementary rotation takes place about a line perpendicular to the radius vector, and lying in a plane containing it and the axis of y. On passing from one medium to another the rotation is not neces- sarily continuous. The only surface conditions are that the displace- ments and the stresses are the same on the two sides of the surface of separation, and if the rigidity of the ether be diflPerent in the two media the rotations will be different also. But Professor Stokes's solution does not apply to this case, and for the case to which it does apply is complete. Chapter VII. — The ScATTERrao of Light by Small Particles. § 1. In his experiments on the light scattered from precipitated clouds of fine matter, Tyndall ' showed that when the particles are sufficiently fine the light emitted laterally is blue in colour, and in a direction per- pendicular to that of the incident beam it is completely polarised. The full explanation of this was given by Lord Rayleigh in 1871 in a series of papers * having an important bearing on our present subject the relation between the plane of polarisation and the direction of vibration of plane polarised light. Professor Stokes, in his paper on fluorescence,^ had indicated the connection between the two questions. For consider a beam travelling horizontally, and look at it vertically downwards: the scattered light is in great part polarised in the plane of re- flection. If the scattering particles be small compared with the wave length of the incident light, the vibrations in an incident ray cannot be at right angles to those in a scattered ray. For the incident vibrations are affected by the dust particles, which in consequence of their very great mass relative to the ether remain practically at rest. We may treat the problem as if the dust particles moved exactly as the ether which they replace would do, and then superpose on this motion an equal and opposite motion. The first motion will not affect the regular propagation of the waves. In consequence of the second the particles become centres of disturbance, and set up other motions in the ether. These other motions will depend on the direction of apparent motion of the dust particles, and the optical effect in any direction will depend on the component of the motion at right angles to that direction. Now, the reflected ray is polarised in the plane of reflexion. If, then the > Tyndall, Phil. May. (4). vol. xxxvli. = J. W. Strutt, ' On the Light from the Sky, its Polarisation and Colour,' Phil Mag. Feb. and April, 1871 ; ' On the Scattering of Light by Small Particles,' June, 1871. » Stokes ' On the Change of Refrangibility of Light,' Phil. Trans. 1852. 208 EEPOKT — 1885. vibrations be in the plane of polarisation they will be at right angles to those in the incident light, while if the vibrations be at right angles to the plane of polarisation, they will come from the component of the original vibration, which is at right angles to that plane. If, then, on this supposition as to the relation between plane of polarisation and direction of vibration the incident light be polarised at right angles to the plane of reflection — i.e., in the case before ns in a horizontal plane — the light scattered in the vertical direction should vanish, and this is found to be the case. This general reasoning is substantiated by Lord Ray- leigh in the papers before us by mathematical reasoning, and, moreover, he shows that the intensity of scattered light in any direction varies inversely as the fourth power of the wave length. This may be seen from a consideration of the dimensions involved. The ratio of the two amplitudes in the scattered and incident vibra- tion will be a number. It must also involve the volume of the dust particles, being directly proportional to it, and it also will be inversely proportional to r, the distance from the disturbance ; it must therefore depend on T/X^r. The mathematical expression for the disturbance is found as follows: — Let D' be the density of the ether in the dust particles, D in the space surrounding them. Let the vibrations in the incident wave, when they o strike the dust, be given by A cos — hf. Then the acceleration is -^c^^ bycos^u. In order that the wave may pass on undisturbed through the parts where the density is D', force would require to be applied ; the amount of the force will be - AiD' - B) f ^y cos ^bt per unit volume, and hence a force A(B' -T>)(^y cos ^^bt, conceived to act at O, the position of the particle, gives the same disturb- ance as is caused by the particle. Now, we have seen in Professor Stokes's paper that a force F cos — bt per unit of volume produces a displacement at any other point given by y F sin a Stt ., , . which is this case comes to C = A — ^^ — -— ^ sin a cos -^{ht — r) . . . (90) where n is the angle between the radius vector r and the direction of the force F, and the displacement takes place in the plane passing through the directions of the force and the radius vector, and is at right angles to the latter. ON OPTICAL THEORIES. 209 Lord Rayleigh's paper conclades with another proof of the formala which gives the motion due to a force acting parallel to the axis of z. Pat for the force Ze"", then the equations of motion become, when expressed in terms of the rotation, Hence dij ' (62v2+7i2)a,o = -f^| dz I ]z|(^) ...... (91) 47r6'^ 2^ A and the integral extends over the space T, through which the force where h=^-='l A h' acts Within this space -^ri—-\ is sensibly constant ; and if w be the re. sultant rotation which will take place about an axis perpendicular to the plane through z and the radius vector, tl-TZ sin a e-'*'' w ==■ — . Hence ^= f c.cir= 'Lf smj« cos ^-(W-r) . . (92) J 47r6''r A In the second paper mentioned above Lord Rayleigh points out that the cause of reflexion may be diminished rigidity rather than increased density, and that in this case a scattered ray might be composed of vibrations perpendicular to those of the incident ray ; he then proceeds to_ describe experiments on the composition of the light of the sky, made with a view of showing that it is such as would result, according to the above formula, from light scattered by small particles. And in the third paper he discusses the motion in an elastic solid in which the density and rigidity vary from point to point. The problem is solved for two media differing slightly in density and rigidity, and it is shown that in a direction normal to the incident ray the rotation in the scattered ray, when the incident vibrations are parallel to z, is given by where J3 = Hence, if A« and aD are both finite, the scattered light can never vanish in a plane normal to the incident ray. 1885. ^ P 210 REPORT— 1885. Now we know from experiment that it does vanish, and hence either An or aD must be zero. If we put aD=0, it can be shown from the general expression for the rotation that there are six directions along •which the scattered ray vanishes, for the components of the rotation are given by — An yz ^3 = - P — -'a- r r^ . . . . (94) '"l = p An n ,.2 = p An i- — . ,.2 Wj n ,.2 Now, there is nothing in the experimental results which at all leads to such a conclusion. If the hypothesis of a variable density be adopted, and A n be put zero, then, W3 = AD y '^'^l' D r\ (95) aD x\ ^2=P -p, - -U r and the light vanishes in one direction only, viz. that of the axis of z. This result, of course, agrees with that of the former paper, and we must conclude that Fresnel's explanation of the cause of reflexion is the true one, while MacCullagh's is false, and that in plane polarised light the vibrations are perpendicular to, not parallel to, the plane of polarisation. The theory as left in this paper does not explain the phenomenon of the residual blue discovered also by Tyndall, who found that at a certain stage in the growth of the particle causing the scattering some light is discharged by the cloud parallel to the direction of vibration of the incident light, and that this Hght is of a very intense blue tint. Lord Rayleigh points out that this may be due to the higher powers of aD/D, which have been omitted, and in a more recent paper, based on the electro-magnetic theory, he develops this point more completely.' Chapter VIII. — General Conclusions. § 1. Space compels us to conclude with this the general account of recent work on optical theories based solely on the elastic solid theory. Special problems of various kinds have received their solution, but to these we can only allude ; indeed, for several of them the general proper- ties of wave motion with the principle of interference are all that are required. Such, for example, are the papers by Prof. Stokes, ' On the Theory of certain Bands seen in the Spectrum,' ^ ' On the Formation of the Central Spot in Newton's Rings beyond the Critical Angle.' ^ — This is shown, as was suggested by Lloyd, to be due to the surface disturbance, which takes the place of the refracted wave when the angle of incidence > See p. 2.53. =" Stokes, Phil. Trans. 1848 ; 3Iath. and Phys. Pajiers, vol. ii. p. 14. » Stokes, Caml. Phil. Trans, vol. viii. ; Math, and Phys. Papers, vol. ii. p. 66. ON OPTICAL THEORIES. 211 •exceeds the critical angle. — 'Oa the Perfect Blackness of the Central Spot in Newton's Rings, and on the Verification of Fresnel's Formulse for the Intensities of the Reflected and Refracted Rays.' ' In this paper is ■given the now well-known proof of Arago's law that light is reflected in the same proportion at the first and second surfaces of a transparent plate. 'On the Colours of Thick Plates,' ^ and ' On the Composition and Resolu- tion of Streams of Polarised Light from diSerent sources.' ^ In his ' Investigations in Optics, with special reference to the Spectroscope,' published in the ' Philosophical Magazine ' for 1879 and 1880, Lord Rayleigh has considered the application of the principles of the wave theory to geometrical optics, and the construction of optical instruments. A full account of these is given in the article ' Optics,' in the ' Encyclopsedia Britannica.' Professor Stokes's great paper on Fluorescence '' is chiefly experi- mental. The cause of the phenomena is assigned to the vibrations set up by the incident light in the molecules of the fluorescent substance, which themselves react on the ether and emit the fluorescent light. According to Stokes the vibrations in this light are never of shorter period than those in the incident light; and he in a general way endeavours to account for this, and shows that if the force acting on a given matter molecule due to a given displacement be proportional to a positive inteoral power of the displacement other than the first, then the amplitude of°the displacements would involve the period, and there would be a tendency to increase the amplitudes of vibrations of lower period than that of the incident light, and to decrease the amplitudes in the case of vibrations ■of higher period than that of the incident light. Thus, in a group of disturbed molecules we should expect all possible periods between two, the upper corresponding to the refrangibility of the incident light, the lower corresponding to the natural period of the molecules. This result, known as Stokes's law, has been the cause of much discussion. Some physicists 5 hold that they have found fluorescent substances which con- stitute an exception to it, while others," who have carefully repeated the •critical experiments, draw conclusions in accordance with the law ; and the weight of the evidence is with the latter. A general account of the principles of the elastic solid theory was given in his lectures at Baltimore last year by Sir William Thomson.^ To these we shall return in the next section. § 2. In concluding this part of the report we may say, then, that while the elastic solid theory, taken strictly, fails to represent all the facts of experiment, we have learnt an immense amount by its development, and have been taught where to look for modifications and improvements. We may, I think, infer that the optical diff'erences of bodies depend mainly on differences in the density or effective density of the ether in those bodies, and not on diflPerences of rigidity. Fresnel's general theory •of the cause of reflexion is thus seen to be true, and Green's theory of ' Camh. and, Buh. Math. Journal, vol. iv. ; ilatli. and Phys. Papers, vol. ii. p. 89. ^ Camh. Phil. Trans, vol. ix. a Ihld. * Stokes, ' On the Change of Refrangibility of Light,' Phil. Trans. ' Lommel, Pofjg. Ann. t. 143, p. 1.59 ; M'ied. Ann. t. iii. viii. x. ; Lubarsch, Wied. .Ann. t. xi. « Hagenbach, Poyrj. Ann. ; Lamansky, Journal de Phi/siqve, t. viii. ; Wial. Ann. t. viii. and xi. ' Thomson, Lectures on Molecular Dynamics. P2 212 EEPOiiT— 1885. reflexion and refraction can be made to agree with experiment by the simple supposition that for longitudinal and transverse disturbances respectively, the ether in a transparent body is loaded differently. This same theory of the loading- of the ether will not account for double refraction if we assume that the vibrations are strictly in the wave front. If, however, we admit that in a crystal the vibrations may be normal to the ray, instead of in the wave front, Fresnel's beautiful laws follow at once from the equations given by Lord Rayleigh, which are quite con- sistent with the theory of reflexion and refraction, but there is a diffi- culty in dealing with the pressural wave. Neither of the strict elastic solid theories of Green can be accepted as representing the flicts of ex- periment, and the interesting modification of Green's theory suggested by De St. Venant fails also. In all there are too many constants for the requirements of the experimental results, and the theories do not indicate the meaning of the arbitrary relations between these constants with sufficient clearness and certainty. The suggestions of Cauchy and Briot, with the elegant mathematics ot Sarrau on the periodic distribution of the ether in a transparent body, lead to es:pressions for the relation between the refractive index and wave length which agree well with experiment so long as we steer clear of substances which present the phenomena of anomalous dispersion, but of this they give no account. While the formulaj given by Cauchy and Eisenlohr seem to represent the laws of metallic reflexion witli considerable exactness, the theory on which these formulas rest, requiring as it does a negative value for the square of the refractive index, is inconsistent with the conditions of stability of an elastic solid. Nor is it surprising that a simple elastic solid theory should fail. The properties we have been considering depend on the presence of matter, and we have to deal with two systems of mutually interpenetrating particles. It is clearly a very rough approximation to suppose that the eSect of the matter is merely to alter the rigidity or the density of the ether. The motion of the ether will be disturbed by the presence of the matter ; motion may even be set up in the matter particles. The forces to which this gives rise may, so far as they afiect the ether, enter its equations in such a way as to be equivalent to a change in its density or rigidity, but they may, and probably will, in some cases do more than this. The matter motion will depend in great measure on the ratio which the period of the incident light bears to the free period of tbe matter particles. If this be nearlj- unity, most of the energy in the incident vibration will be absorbed in setting the matter into motion, and the solution will be modified accordingly. Part III. THEORIES BASED ON THE MUTUAL BE ACTION BETWEEN THE ETHER AND MATTER. Chapter I. — The Propagation of Waves through two mutually Interpenetrating Media. § 1. In the optical theories hitherto considered attempts have been made to account for the phenomena of reflexion, refi-action, and dispersiott by the hypotheses of modifications produced in the properties of the ether O.N OPTICAL THEORIES. 213 by the reaction of the material particles of the medium through which the light was being propagated. According to Fresnel the density of the ether is affected, while according to Neumann and MacCullagh it is to •changes in the rigidity that the effects are due. In both cases the direct effects of the communication of momentum from the ether to the material particles of the transparent medium is not considered. Fresnel, ' it is true, thought it ■ probable ' that the molecules of ponderable matter should partake of the movement of the ' ether which surrounds them on all sides,' and Cauchy,^ in one memoir, deals with the motion of two mutually interpenetrating systems of molecules, but without arriving at any specially important result. Voigt' states that about 1865 F. Neumann was in the habit of treating, in his lectures, the system of simultaneous equations relating to the motion of ether and matter. Briot,^ in his work on dispersion, considers the direct reaction between matter and ether particles, but in his final result equates, as we have seen,'^ the term expressing it to zero. § 2. In 1867 a paper was presented to the French Academy by M. Boussine.sq ^ on the ' Theorie nouvelle des ondes Inmineuses.' In this paper the dynamical effects of momentum communicated by the ether to the molecules of ponderable matter are considered as the cause ■of reflexion, refraction, polarisation, dispersion, &c. The ether is treated as homogeneous, and of the same density and rigidity in all bodies, and it is supposed that when light enters a trans- parent medium the molecules of that medium may be set in vibration isochronously with those of the ether. We have thus to consider the forces acting on such a medium, and these may be divided into three parts: (1) those which arise from the elastic reactions of the ether, (2) those arising from the elastic reactions of the matter, and (3) those arising from the mutual action between matter and ether. Now let us consider a small element of volume, containing both matter and ether. Let m be the density of the ether, /< of the matter, u, v, to the dis- placements of the ether in the element, U, V, W those of the matter. Then, using Green's notation, the force, measured parallel to the axis of x, arising from (1) will be per unit of volume — du dv dw where 6 = , ~ + , + -, . dx dij dz d-n For the forces arising under (2) we have to consider that in-jj^ acd d^V . . . fx -j^ ^ill be quantities of the same order ; but ju is very great indeed •compared with m, and hence U is very small compared with u. The ' ' Premier !Memoire sur la double refraction,' OSuvres completes, t. ii. p. 278. ^ Exercu'.cs d'Analjisc, t. i. p. 33. ' Wied. Ann. t. xvii. p. 473. * Jissats sur la theorie mathcmatique de la luiuiire. Paris: 1865. * See p. 181. " C. R. t. Ixv. p. 235 ; Liouville's Journal, s. ii. t. xiii. p. 313. A most clear ac- count of this theory is given by M. de St. Venant in the article already quoted, 'Theorie des ondes lumineuses,' Ann. de Chim. s. ix. t. xxv. p. 368 seq. 214 EEPOKT — ]88o. forces (2) depend on U and its differential coefficients, and it is assumed in the theorj that in consequence of the excessive smallness of U they may be neglected. Again, let us suppose that the dimensions of the ele- ment of volume are large compared with the distance through which the action of an ether particle on a matter particle is appreciable. Then we may consider the mutual reaction between matter and ether as confined entirely to the element of volume considered, the actions taking place across the surfaces of the element will just balance each other, and hence,, if we consider the matter and ether as one system, the force (8) will be- zero, and the equations of motion will be J,. + M ^ = (A-B) ^_^ + B V he, etc. . . (1> m U is here the displacement of the matter occupying the same element of volume as the ether, whose displacement is u, but all the displacementa being very small, it is assumed that we may treat U and u as the dis- placements of the matter and ether, which when at rest occupy the same element of volume. Thus XJ, V, W are functions of w, v, w and their diffe- rential coefficients with respect to x, y, z, the initial co-ordinates, and may be expanded in terms of these, and it remains to find the form of the expansion. Conditions are, of course, imposed by the fact that the medium is isotropic, and it is shown that so far as second differential coefficients Me may write U = An + C ^^^ -I- D v^w, etc. . . . (2) On substituting this value of U, in the equation of motion, and assuming; Stt / m.r + tip + pz\ H = Me ' ^ V ~ "> ) etc., we obtain And these equations, of course, give a normal wave travelling with a velocity [ {X + 2^1 + 4(C + D) tt^, /r^} /(p + Ap,)]\ and a transverse wave with velocity [ {p -h4D7r2p,/r2} /(p -f- Ap,)]--. These velocities vary with the period of vibration in a manner which agrees, at least approximately, with experiment. It is clear that the coefficient A is positive, while the experimental fact that the velocity increases with the period shows that D is negative. The condition that A is positive merely implies that the ether tends to move the matter particles in the same direction as it moves in itself. If we suppose that the medium is not isotropically symmetrical, while at the same time it is such that the expi-essions retain the same form when two of the axes are turned through a small angle about the third, then terms B (-- — _-) come into the value for U, and these, it is shown^ \ dz ay J would cause the medium to produce rotation of the plane of polarisation of a plane polarised ray traversing it. This rotation would vary approxi- niately inversely as the square of the period, in accordance with the law discovered by Briot. By introducing higher differential coefficients into. ON OPTICAL THEORIES. 215 the value of U in terms of u, etc., it is shown that these approximate laws become, respectively, -=v„^(i + ^;+i;; + (4) V being the velocity, and Vq, £, etc. constants, while for \p, the rotation produced by a length z of the substance, he finds ^=H 1 + f f" o * 4 ' (5) For the explanation of double refraction Boussinesq supposes that the constants in the above formula giving U, V, W in terms of u, v, w may be functions of the direction of displacement ; but, arguing from the relative importance of A, C, and D in the ordinary theory of refraction (refraction is due to the existence of A, dispersion only to that of D), he supposes that we may to a first approximation treat C and D as constants, while we consider A as a function of the direction, and write for the three axes of symmetry, the existence of which is assumed, the values A(l + a), A(l + /3), and A(l + y). This leads to the equations — |i'=K(l + .)| + L(l + «)v'„ 4!£ cPw K(l + 6)f- + L(l + h)^'v ax :K(1 + C) ~+U]. +C)V^W ax / (6). K, L, a, 6, c being functions of the other constants. It is clear that these are the same equations as were given by Lord Rayleigh,* and ■which have been already considered. The wave surface they lead to is not Fresnel's, at least if we suppose the vibrations to be necessarily transversal. By retaining the terms involving the coefficient B, the elliptic polari- sation produced by quartz in directions oblique to the axis is explained. The formula for the difference in velocity in the two elliptically polarised waves traversing the crystal in any given direction agrees closely with that given by MacCullagh. In this case the squares of the velocities parallel to the axis are given by the expression N f 1 ± — r^ J , while the ve- locities in a direction making an angle with the axis depend on the equation w- = N + — pr — sm'' t) + — -— ± |a/[(M - N)2 sin^ 9 +^-^ I 2N + (M - N) sin^ j 1 . (7) > See p. 179. 216 EEPORT — 1885. wbicli can also be expressed in terms of the principal velocities at right angles to the axis, for if w,, wj be the valnes of these, we have M + N = io,^ + u}'- (M - N)2 = (o 2\2. ') (w,2 + Wo") (8) The laws obtained in this paper are further developed in a second and third in the sanae joui'nal. In this third paper, Bonssinesq ' points out the necessity of including in the expression for U in terms of u diflFerential co-efficients of u, v, iv with respect to the time, and shows that the phenomena of magnetic rotation can be accounted for by putting in the case of a wave travelling parallel to z — U =Au dt V = A^- + 33 '~ dt W=: Aw (9) while the phenomena presented by refraction at the surface of a moving body are explained on the supposition that in finding d?\] jdP we have to take into account the visible motion of the body, and write d dt \ d , T d — + JU — - dt dx + M f + ay o (10) L, M, N being the components of the velocity at the point x, y, z ; it is shown that in cases in which L, M, N are small compared with w', the apparent velocity of light in the body is o' = w + 2 ' ' yu being the refractive index and V the velocity of the body in the direction in which the light is travelling. This, of course, is the formula given by Fresnel. § 3. M. de St. Venant,^ in the article already quoted, sums up his criti- cism of the theory as follows : ' Les deux hypotheses principales de cette theorie nouvelle me semblent bien pres de s'elever a la hauteur de choses demontrees.' At the same time tbere remains the difficulty pointed out by Sarrau ^ of explaining on mechanical principles how the various terms in U, V, W arise, and on what physical phenomena the mechanical forces brought into action depend. § 4. A further step in the progress of the theory was brought about by the discovery of anomalous dispersion by Christiansen ■* in 1870. Le ' Bonssinesq, Liouville's Jounml, t. xiii. pp. 340, 425. - De St. Venant, ' Sur les diverses methodes de presenter la th6orie des ondes lumineuses,' Ann. de Chimie, t. xxii. ' ' Theorie des ondes lumineuses,' Ann. de Chini. (4), t. xxvii. p. 272. * Fogg. Ann. t. 141, p. 479 ; t. 143, p. 250. ON OPTICAL THEORIES. 217 Roux ' had found that vapour of iodine refracted red light more strongly than violet, and Christiansen, in the paper quoted, announced the result that for a solution of the aniline dye fachsin in alcohol the refractive index increases from the Fraunhofer line B to U, then sinks rapidly as far as G, and increases again beyond. The experimental investigation of the subject was continued by Kundt,^ who proved that this anomalous dispersion was marked in all substances showing strong surface color- ation, and that there was an intimate relation between it and the absorptive power of the substance. As the result of his experiments, Kundt was able to lay down the rule that in going up the spectrum, from red to violet, below an absorption band the deviation is abnormally increased by the absorption, while above the band the deviation is abnormally decreased. Kundt has been able to see this abnormal effect produced by the absorption of sodium light. On the old theory of dispersion, as developed by Cauchy and others, this effect was inexplicable. Boussinesq, it is true, had explained the phenomena in vapour of iodine by saying that it implied that the co- efficient D was positive ; and here, in a way, lay a germ of the truth, for the mutual reaction theory lends itself readily to a partial explanation of the whole. § 5. Such an explanation was first given by Sellmeyer. He had been led to expect the effect from theoretical reasons in 1866,' and had endeavoured to discover it in a fuchsin solution, but without success. The action between the ether and matter is a periodic one of the same period as the light- wave traversing the ether. Owing to the enormous density of the matter compared with the ether its motion will in general be negligeably small ; but if it should happen that the period of the natural vibrations of the matter particles coincides with that of the incident disturbance this will no longer be the case. The energy of the light- vibration will be absorbed by the matter, and this absorption will tend to react on the light-disturbance, and will, it can be shown, increase the refractive power of the medium for disturbances of greater period than the critical one, and decrease it for disturbances of less period. The problem is much the same as that of a pendulum the point of .support of which is undergoing a small periodic disturbance. If the period of the disturbance be greater than that of the natural vibration of the pendulum the reaction of the pendulum on its support will tend to quicken the motion of the latter, and vice versa. Sellmeyer, in the papers referred to,^ published in 1872, after a most clear and able discussion of the difficulties of the elastic solid theories, adopts the hypothesis that the ponderable atoms vibrate, but with much smaller amplitudes than the ether particles. He then proceeds to consider the mechanism by which this is brought about. As with Boussinesq, the ether is supposed to have the same rigidity and density everywhere. The ether particles act directly on the matter particles, and in consequence of the vibrations of the former the equilibrium positions of the latter are ' Ann. de Chiiii. S. III. t. xli. p. 285. = Poffff. Ami. t. 142, p. 163; t. 143. pp. 149, 259; t. 144, p. 128; t. 14.5, pp. 17 and 164. ^ Sellmeyer, Por/ff. Ann. t. 142, p. 272. ■* SeUmeyer, ' Ueber die dxirch die ^5i;tlier-Schwingungen erreg^en Mitscliwingungen der Korpertheilchen und deren Kiickwirkung auf die erstern, besonders zur Erklarimg der Dispersion und ihrer Anomalien,' Poffg. Ann. t, 145, pp. 399, 520; t. 147, pp. 386, £25. 218 BEPORT— 1885. disturbed and execute small harmonic vibrations ; but the matter par- ticles themselves vrill not generally coincide with their positions of instantaneous rest, and so we have to consider their vibrations about these positions. The equilibrium position of the matter at any instant is made to depend on the configuration of the ether at that instant, and may clearly be expressed, under the given circumstances, as a simple har- monic function of the time, so that if soi Vo (o be the equilibrium co- ordinates at time < of a given matter particle of mass m', we may put ^u = «„ sin 27r ^ .... (liy r The ampUtude a^ will be very small. The force acting on the particle m' is then considered on the assump- tion that the action between two particles of ether and matter respectively depends solely on the distance, and may be expressed by mm'f(r), and it is shown that, supposing that/(r) is a continuous function of the co-ordi- nates,' the force per unit mass tending to draw in' to its instantaneous position of equilibrium is X=^%^-.^o) .... (12> where c is a quantity depending on /and the configuration of the medium, which may be a function of the direction. Thus, for an isotropic medium we have as the equation of motion of the matter particles — = - r^\^ -ftflSin ^ + ci) |, which leads, of course, to the integral i=-:^^aosm^(t+a) + hsm^l(t + ft) . . (13> t' — c r except when r^^, when t, = — TT - ttQ COS ^(r-La) -r 6sin ^ (t + l^) • • (14) t d d The question as to the legitimacy of the assumption involved in the equation tQ = ttg sin — {t + a) T is then discussed, and it is finally shown that it is correct. Again, it follows with great probability, from the experiments of Fizeau and Foucault ^ on interference with long difference of path, that in a ray of light the amplitude of vibration resolved in a given direction is not constant. We have, therefore, to treat a^ as varying — slowly, it is true,, compared with the rapidity of the vibrations — but still, it is probable, passing through many series of changes in one second. This leads to the result that h, the amplitude of the natural vibrationa ' See Stokes, Srit. Assoc. ReiioH, 1862, p. 261. "^ Ann. de Chim. s iii. t. xxvi. p. 138. ON OPTICAL THEORIES. 219 of the matter particle, will always be small unless r = c. Omitting, then, these from consideration, it follows that _2 t' — c^ and the vibrations thus set up in the matter are shown to be the cause of refraction ; while if r = c we have ^= —a cos 2:7 , da_. ^ . . . . (16). and these vibrations are the cause of absorption. So far, then, the results of this investigation agree with those Bonssinesq has given. They are, however, more general, in that they contemplate the possibility of the motions of the matter particles becoming appreciable, and so producing absorption. The next paper considers the question of the manner in which the action between the matter and ether aflects the velocity of light. At 6rst the direct efPect of the matter on the ether is neglected, and the refractive power of the substance is found by considering the energy lost by the ether and gained by the matter in each vibration. The refractive power is measured by n'^ — ], where w is the refractive index. Now consider a volume so small that all the ether particles in it may be treated as in the same phase, so large that it contains many matter particles, and suppose the reactions considered confined to the ether and matter of this element. Then it can be shown that if m' be the density of the ether, a' the ampli- tude of its vibration, the energy lost by the ether is (n^ — l)2x'^m'a'yT'^, while that gained by the matter is 2Tr'^ [Imr'^at)'^ J(t^ — c^)] jr^, whence the important formula r.2 S-J/l-r -Mn^ „.-! = ^^!:i .... (17). is obtained. We may write this — ,2_1 V 1=Z r 1- <^«> where by E we mean that all the possible values of S, the free period of the matter particles, are to be taken into consideration. Now let us suppose that r is greater than c, and that the matter particles have only one free period, then the denominator of the fraction is positive, and decreases as r approaches c. The refractive power, therefore, increases as the period decreases (i.e., as we go up the spectrum), and as t approaches the critical value c (i.e., as we near the absorption band) the refractive power is abnormally increased. Above the absorption band, supposing there be but one, the fraction is negative, and decreases numerically in value as r is still further decreased ; and until r reaches a value for which l/r^ = l/o^ + K, n is imaginary. ^^^ EEPOKT — 1885. As r decreases Still further the refractive power increases, but the refractive index is less than unity. The presence of a second absorption band above the first will of course, modify the conclusions. The change in refractive power is perhaps best illustrated by a curve, as is done in Sellmeyer's paper For the case above considered take values of the refractive power (n'-l) tor ord.nates and the reciprocals of the periods for abscissfB, then the equation in the case of one absorption band will be where a = i/c^ Thus the curve is an hyperbola, with the axis of .r and the line a; = a as asymptotes. If there be two absorption bands we have K , L y= — +i^. a—x b — X and in this case there would be two critical values for x (viz., a and h) for which the refractive power would become infinite, and near which the dispersion would be anomalous. In 1874 there appeared a paper by Ketteler i on the same subiect. the^fm^muir' ''^^^'" enunciated as the law of dispersion in a gas n^-} = ^ 0' 1 I being the wave length and o, ft constants. I^urther comparison with experiments had led him to the formulaj l=Kr- + A+ — ~ and he now shows that by a proper interpretation of the constants this wilJ include the case of abnormal dispersion, § 6. The theory of the mutual reaction between the matter and ether was next developed by Helmholtz, and his work was continued by Loramel, Ketteler, and Voigt. The method adopted by Ketteler differs somewhat from tiiose of the other three. Helmholtz ^ (in 1875), LommeP (m I87&), and Voigt -» (in 1883) start in the same manner to form the simultaneous equations satisfied by the displacements of the ether and matter particles in a given element of volume. Let n, v, w be the dis- placements of the ether particles of density ni in an element of volume cv, U, V, W those of the matter particles of density ^i. The forces on m are, as in Boussinesq's paper referred to above,-^' ■considering only the components parallel to the ,«axis :— Ar,l, ^f^^}t^''^^^^lT'H^^^?''^^^^ aer sogenannten anomalen Dispersion,' Paw. ^WM. Jubelband, p. 166. See also p. 181. \ Helmholtz, ' ZurTheorie der anomalen Dispersion,' Pog,/. A^m. t. 1.5i, p. 582. p 339 Theorie der normalen und anormalen Dispersion,' ^ned. Ann. iAii. * ^oi&t, Theorie des Lichtes fiir vollkommen durchsichtige Medien,' Mied. Ann. X, Aix. p, o7o. * See p. 213. ON OPTICAL THEORIES. 221 (1) X', arising from external impressed forces ; (2) X, arising from the action of the other ether particles external to- the element cv ; (3) A, arising from the action of the matter. "While for fi, the matter particle, they are : — (1) S', arising from external impressed forces ; (2) ^, arising from the action of the matter external to the element ; (3) A, arising from the direct action of the ether. So that the equations of motion for an isotropic medium are — j^^ = X' + X +A. etc. 1 m'—rir = -^ + A + A, dl^ etc. (19> a^' In all three theories the impressed forces are supposed to vanish, so that X' = S' = 0. The action between the matter and ether is supposed to be confined to the element of volume considered — i.e. the dimensions of the element are treated as large compared with the distance at which the direct action of an ether particle on a matter particle is sensible. This leads to the relation' J. + A = 0, independently of the value of^. The term X springs from the ordinary elastic reaction of the ether. Helmholtz and Lommel, considering only a wave of displacement in the direction of x travelling parallel to z, write for this term while Voigt considers the general forms of the expression given by the ordinary elastic solid theory, which, of course, reduces for the case of an isotropic medium to e V ^M + e' — , ax where 5^ du , dv , dw = — + — \- — . fZ« dy dz For the forces represented by S, Voigt again considers the general case of a strained elastic solid, while Helmholtz and Lommel after him write >—l 9TT *> "' U Tor the proper values to be given to A and A there is great divergence of opinion shown in the three theories. ' In his paper Lommel — as has been pointed out byJKetteler, ' Optische Contro- -^ersen,' Wied. Ann. t. xviii. p. 387, and "Voigt, ' Bemerkungen zu Herrn Lommel's Theorie des Lichtes,' Wied. Ann. t. xvii. p. 468— really employs the condition ^ - A = 0, for he estimates « and U in opposite directions. In his reply, Wied. Ann. t. xix. p. 908, Lnmmel endeavours to justify the signs used, but I think witliout success. The- effect will be to change the sign of a coefficieEt in one of the terms. 222 REPORT — 1885. Helmholtz supposes, ' um die Bewegungsgleichungen zu vervoll- stjindigen,' that A is proportional to the relative displacement of the ether and atoms in the element of volume, and writes, therefore, A = /32(U- ?0- Lommel supposes that the action ' follows Newton's law of friction,' and depends on the relative velocity of the two ; he puts, therefore, A^fi'^CU-u). at The expression given by Voigt is much more complicated, and can iDest be considered later. Thus the equations we have to deal with are — (Helmholtz), and ,|y=-,j>(n-„)-«'u-v'^;^ (20) ctr dz^ dt (I'll 9 a-U , -„)(l ,-r~r > (^2U ,.2''^TT ^ 2TT 2 ^?U* (21) (Lommel). The method of solution is the same in both, xi and U, which, strictly, are the displacements of ether and matter in the same volume in the dis- placed condition, are treated as if they were the displacements of ether and matter having the same undisturbed co-ordinates «;, if, z. This is legitimate, for U and n are both taken to be functions of the position of the wave front and the time only, and hence for all points on the same wave front U has at a given instant the same value. Assume, then, U = Ae-''-^ + '•'"-- '■"'■■tj • • • . (22) k is the coefficient of absorption, c the velocity, and 2!r /« the period of the vibration. On substituting these values in Helmholtz's equations, we find and 2^ _ /3*y' en o^T;: (fiH^ _a^_ ^32)2 + ^4,,2 = ^ (say) • . (24) * In this equation tlie sign of 0- has been changed from that given by Lommel in accordance with the remark on p. 221 ; but see Lommel's reply to Voiot Wied -Inn t. six. p. 908. t A, of course, no longer has the same meaning as above, but is the amplitude of the matter vibrations. To solve these, pat ON OPTICAL THEORIES. 223 ] - = |0 COS (t», c h - = p sm (.). n Then 1-^=p'cos2w=f' 2^ = p^ sin 2w = G (25) Thus the value of Jc, on which the absorption depends, is proportional to y^, the coefficient of (T\J jdt in the equation, and vanishes if y^ is zero ; that is, if there be no frictional resistance to the matter motion. If h be •at all appreciable, the light-disturbance will penetrate but a little way into the medium, so that for transparent media we may treat h, and there- fore G, as small. In this case we have ,2 = F+^j^ + ,etc., -while in the small term we may put for G/F the value 2A;c/w. In these circumstances, then, l=\..G-^'y' where ^,2 = a2 + /32_yt/2^] (26) (27) Thus, as n changes kjc is a maximum when n = v; if the corresponding values of k and c be Lq and Co, then i-o I "^ 4^2(^2^ ^2) f-^ • . . (28) If the value of y be zero, then, for n = r, h is infinite compared with c ; all the light is absorbed. At the same time A is large, and we have, in dealing with the motion of the matter particles, to consider the limit of Ae-*o^. Turning, now, to the refraction, let C be the velocity of light in free space, N the refractive index, and suppose that the term ^G^/P may be neglected, then N2 = c^F = ^'" fl - — + /3^(-^ + 2^^-n^) -[ a2 L mn^ m^w2{(,.2_ ^2^)2 + 4^2(^2 + ^2^1 J • y-^y) and the maxima and minima values of this expression lead to the limiting values of the refractive index. These, it is shown, are given approximately by n^ — v'^=±l 2)'«t, which 224 REPOBT 1885. correspond nearly to the maxima of absorption. Thus, as we go up the spectrum, the refractive power is a maximum for the value oi n, given by 7i,2 = ,/2 _ 2 r-nr, and a minimum for 7.^ = r^ + 2)"Z3-. There is, thei'efore, abnormal dispersion in the neighbourhood of the absorption band, but elsewhere the refractive index increases with n. Again, for large values of 11. we have N2 = C^to/o^. Now, if the density and the rigidity of the ether be the same in all bodies, we should have C^ = a^jm, and therefore in this case 1^ = 1. Thus the light of shortest wave lengths would be trans- mitted without refraction, contrary to experimental results. Sellmeyer, however, pointed out a method of explaining this difficulty which would be consistent with t"he supposition that C^ is equal to a^jm. According to him, we must suppose that there is a strong absorption band some- where just above the visible limits of the spectrum — that is to say, that the value of i^ — 2i"st is just beyond the limits of the visible spectrum, and that owing to this the refraction below the band is abnormally increased. The paper closes with a method for constructing the form of the refraction and absorption curves. Lommel's equations can be solved in a similar manner, and lead to similar formulfe. The two theories can best be compared with each other and with experiment by changing the notation slightly, and adopting that used by Ketteler ' in his criticism of the same. Let us put, therefore, a- =, (30) .-.<.. 5)) Then Helmholtz's equations (23) and (24) become ( A-2 m B^O-^^-n^) f.i,nn^{{ro'-n^y + nh'y^ K}. (31) and 2k m B2,5K en a^ fimn ((j-q^ _ n^) + nh'^^K^} (32) and if we suppose X, X,, Xq to be the wave lengths corresponding to the periods n, I'l, and vq, we find B2 X;^ A\2_ _ ;^^~ BX2 , A"« X/VXo' J L f.tm X 2 X2 G = m jim X," "'(^-0- + K2 (33) ' Ketteler, 'OiDtische Controversen,' Wied. Ann. t. xviii. p. 387. ON OPTICAL THEORIES. 225 while the ratio of the amplitudes is given by B X2 ^=^' /^/./'V . -x.-, • ■ • m /{(^-O^-S) We can give a sort of physical meaning to the constants in these formulae as follows : A, is the wave length of the natural vibrations of the matter, freed from any action of the ether; Xq is their wave length on the suppo- sition that the action between the ether and matter is proportional to the displacement, while the ether remains fixed ; while I'l and j'q are the frequencies of these vibrations. B vanishes when there is no matter present, and since the expression shows that B/m is a number, it is probable that B will be proportional to the matter density ; while K is a number on which the strength of the frictional retardation depends. The quantity Xj, the wave length of the free vibrations (i.e. the dis- tance the light-wave travels in a natural free matter period) is immensely great compared with X, so that A is small compared with % except in the cases in which X does not differ greatly from Xq. It will be seen at once that the formula for F, on which, when the absorption is small, the refractive index depends, in terms of the wave length is very complicated. I am not aware that any attempts have been made to compare it carefully with theory. In the cases in which K is small (i.e., for transparent media) Xq will be an approximate lower limit to the wave length of the light trans- mitted. If we integrate the equation given by Lommel's hypothesis, modified so as to agree with the principle of action and reaction, we find F*=^ «2 • (35) where B' is a constant related to the /3- of Lommel's equations in the same manner as B is to jp above. If, however, we take Lommel's ex- pression strictly, to which he still adheres,' the sign of the fractional expression must be changed. If we retain the negative sign the formula (35) fails to represent the facts. Neglecting for a moment the effect of absorption, and supposing the ether to be of the same rigidity and density as in free space, the square of the refractive index will be rather less than unity for the longest waves ; it ■will then decrease to a minimum value, which will be positive, and then rise rapidly through the absorption band, for which X = Xq, reaching a maximum a little above the band, from which it will again fall. Absorp- tion efifects will only slightly modify these conclusions. Thus the spectrum above the band ought to be more refracted than that below, and except just near the band the refractive index should decrease as the wave length decreases. This is fatal to the theory in this form. In its * This becomes the expression given by Lommel on substituting B'/m — K = €=, ^i" \. B' =wi(K — €), and interchanging m and /x. ' Lommel, ' Zur Theorie des Lichtes,' M'ied. Ann. t. xix. p. 908. 1885. Q 226 KEPOBT— 1885. original form it is not open to this criticism, and accounts for the facts, bat its fundamental equations are hopelessly at variance with Newton's third law, so long, at least, as we suppose the mutual reaction limited to that between the matter and ether in the element of volume considered — that is, so long as we may suppose that there are many molecules in an element of volume. The original formula for dispersion leads to results which, as Lommel ' has shown, agree fairly with experiment ; and by carry- ing the approximation a step further the agreement becomes closer still, so that his fundamental equations might be taken as an empirical repre- sentation of the facts with some approach to the truth. Voigt's theory differs from these mainly in the values assigned to A and A and the methods by which those values are obtained ; and before treating at length of it, it will conduce to clearness if we consider Ketteler's theory, the results of which have considerable resemblance to the two already mentioned, while the work itself is earlier than Voigt's. § 7. Ketteler ^ is the author of a large number of papers on this subject, and the form in which he has presented his theory has varied somewhat, though the central idea which he has endeavoured to express has remained the same throughout. The idea seems to be as follows. The exact expression of the action between matter and ether, the A and A of the fundamental equations, is unknown to us, and we must therefore endeavour to eliminate it from the equations. This we can effect by con- sidering the work done per unit time on the whole system, into which, of course, the mutual reactions will not come, and equating it to the rate of change of the kinetic energy. This alone, of course, will only lead to one equation, and though in some of his work Ketteler appears to obtain two out of it, this, as we shall see shortly, is done by the aid of an additional hypothesis. It is, however, not till some of the later papers that these views are completely developed. In his first paper ^ he assumes that the action of the matter on the ether is to increase its rigidity by the quantity ea, and to introduce a resistance acp, where £ is constant for the medium and a is some unknown function of its dynamical condition, while the forces on the matter are a(£' v^p' + kV')> f' being the matter displacement, so that, considering the motion parallel to x, we have for the ether and for the matter \- . ■ . (36) Arguments similar to those employed by Sellmeyer lead to the equation N2-l = ^ (37) and on multiplying the first of the equations of motion by p, the second ' Lommel, ' Ueber das Dispersionsgesetz,' Wied. An?i, t. xiii. p. 353. ^ Since the above was sent to press, Ketteler has published his optical theories in the form of a book, Theoretische Optik : Braunschweig, F. Vieweg und Sahn, 1885. The fundamental equations are formed as indicated below (Equation 43), and the remarks made in connection with that section apply. ' Ketteler, 'Versuch einer Theorie der (anomalen) Dispersion des Lichtes in einfach- und doppelt-brechenden Medien,' Carl Repertoriwrn, t. xii. p. 322. »» ^7r= (« + «°) -A + "^P ON OPTICAL THEORIES. 227 by p\ we find that the condition (37) reqaires the coeflacient of a to vanish separately, and we are led to the two equations (38) and these are the two fundamental equations of the theory, from which an expression is found for the refractive index in terms of the wave leno-ths and constants, viz. : — ° N2 = N»^ +^v^ (39) — -1 \' wrhere the S must be taken to include the different kinds of matter |)articles m the medium. So far, at any rate, the theoretical bases ot these expressions are no more secure than those of Lommel and Helm- holtz. Ihe dispersion equation, however, is much more simple than that given by Helmholtz, and agrees well, as Kefcteler i has himself shown with experiment. A second paper 2 develops some further consequences and traces the torm ot the dispersion curve in various circumstances. In a third paper ^ the principles of the theory are stated and applied to doubly refracting media, but the equations from which he starts- the same as those given above, only written with three co-ordinates— do not express the physical facts which they are intended to do, and the theorv deduced can only be considered as empirical. A further attempt, based on this principle of energy alone, is made in a more recent paper ' to establish two independent equations Thus the ether mass in an element being displaced a distance ds, the matter mass •as ; then the equation '»i?*+-'s^*' = «S* . . . (40) IS supposed to express the law of the conservation of energy for the ether motion ; it neglects entirely the forces on m' from the action of neiffh- ftouring matter. The conservation of energy principle alone will ^ive but one equation when applied to the system, though it will of course eliminate the unknown reactions between matter and ether w,-fl T^^'^ remarks must be made with regard to other papers ^"^ dealing with the formation of the fundamental equations. The equations D of tne last article referred to are only true on the assumption that the ' See p. 181. Ann^^lioTv-'m^ Zusammenhang zwischen Absorption und Dispersion,' P^^^. breclSn Mit'tpl'n ''2''°"^/''i?''?'''^°^ und Absorption des Lichtes in doppelt- orecnenaen Mitteln, Pogfi. Ann. Erganzung, Band viii. p. 444. 5 -^^f 1 .'Su' I^^spersionsgesetz,' Wied. Ann. t. vii. p. 658. AMd £r mJ ..?^n ^r ^^^o^'^^^iiden Anisotropen-Mittel,' Mo7iatsier. der Koniql. t S n 387 -KrwS '"' ^°^.i^' ^^ 'Optische Controversen,' Wied. Ann. X. xviu. p. 387 , Erwiederung auf Herrn Voigt's Kritik,' Wled. Ann. Bd. xxi. p. 178 Q2 228 BEPOET — 1885. reaction of the matter on the ether produces a force —m'C — ^* while the action of the ether on the matter is expressed by a force — m C — ^• and, indeed, in his most recent work on the subject ' he realises clearly that the energy principle only leads him to one equation, viz. : — m -^dp + m' — ^- dp' = e\7^pdp — icp'dp' . . (41) e being the rigidity of the ether in free space — and then combines with this a ' second equation relating to the special mode of action of the matter particles, which can be no other than the renowned fundamental equation of Bessel's theory of the pendulum ' ; this may be written It is then further assumed that the matter particles exert a force /jm'p' on the ether, and the equations finally become — »i§-m'Co^'=evV+A»y 111 'c f^V , ,„/ dy _ /,,„/ : ., <ip' C dt . ,dy ( , . dp'\ (43) leading to the equation N^-Ki = N^^- No'+V-l(Nl -l)K^' ~\ ,^-iw-ikA (44) ■where K is a quantity depending on y. When K is small, as is always the case in transijai-ent media, this becomes the formula already men- tioned, which has been tested over so wide a range by Ketteler. It is clear from these last equations that the action of the matter on the ether is represented by ?)i'Co'-ri- + P^i'p', and of the ether on the matter by in ^ T^ jg (Jifficult to conceive of the mechanical principles which ° df^' would lead to these terms as they stand, and the occurrence of the imao^inary quantity in the expression for the refractive index, to which they lead, is a blot on the theory. § 8. In fact, the form of the equations given in his earlier papers ^' leads to results which are more directly intelligible, while the equations themselves can, it seems to me, be established by the aid of a suggestion due to Ketteler himself (' Eine dritte Annahme,' p. 397). For, taking the notation employed when considering Helmholtz and * In Ketteler's paper ^, |' are used for the displacements. I have retained p, p', in accordance with the notation ah-eady employed. ' ' Zur Dispersionstheorie des Lichtes,' Wied. Ann. t. xxi. p. 199. See also Ketteler, TheoretiscJie Ojdilt, p. 85, et seq. ' Ketteler, ' Optische Controversen,' Wied. Ann. t. xviii. p. 387. ON OPTICAL THEORIES. 229 Lommel, let us assume, according to this third supposition of Ketteler's, that the reaction between the ether and matter is proportional to the relative accelerations of the two. Helmholtz supposes it proportional to the relative displacements, Lommel to the relative velocities. In this <jase, then, and hence A=-/3^J^(.-U), m5^+/32^^(t,_U)=.N, <P Thus 7)1 iVy, _ fihn d^XJ _ mX ■n 7W. + /32 dt^ m + /32 2 ,lfi ^ /- ,7/2 — .. _ ,'2 df' dt^ P-P' (45) (46) And, with Ketteler's assumptions as to the forces X and ^, these may be written as follows — d-n „, d<2 .(Pu dz^ (....f)j (47) which are the same in form as Ketteler's equations, though a^ is not the rigidity of the free ether, while there is a relation between C and C, for and C'=-'^. c = fi m + jy^ ft' (48) However, this does not matter, for it is the product CC which comes into the fundamental equations of the solution, and we find 2 1 7-2 in L. °(^-0 ( 1)%K^^^ A,^ 2k VI y en DK?- K2 ^2 (49) (50) where D = CC, and K is proportional to y^. The quantity a^/m is no longer the square of the velocity in free space, and cannot be put equal to unity, and, in fact, a'^/vi will be the square of the refractive index for very long waves. Ketteler (p. 398) 230 EEPORT— 1885. seems to consider it an objection to Lis theory that it gives a value dif- fering from unity to the refractive index for infinite waves, but the objec- tion is not, I think, serious. As has been stated before, the dispersion equation given by his theory has been repeatedly tested by Ketteler,' and the agreement between theory and experiment is very satisfactory. . Thus we may probably look upon this equation as one established em- pirically by his experiments, and while not agreeing with the reasoning- employed by Ketteler in forming his equations of motion, may see in those equations the expression of a possible law of action between matter- and the ether. § 9. Let us now turn to Voigt's work, which is of more recent date. He has been a severe critic of his predecessors, and objects strongly to various points in their work. In his first paper ^ on the subject Voigt, following Boussinesq,^ remarks that mtVuliW and /jid^U Idi^ being quantities of the same order, U will be very small compared with u because fi is very large compared with m ; it is therefore not necessary to introduce terms involving U into the diiFerential equations for u. To this we may reply, (1) that it is quite possible that the coefficients of U and its differential coefficients- involve fi the matter density, and that in consequence the terms in ques- tion are comparable with md^itjdt^, and (2) that in the critical case near the absorption band the value of U becomes large, and may be quite comparable with ii. Voigt also objects to the form adopted for S in all the previous theories, viz. — (kU + ydV jdt), pointing out that Helmholtz introduced the kU ' zur Vereinfachung der Rechnung,' and the ydV/dt to explain the transformation of light-energy into heat. If the ponderable matter is to be looked on as an elastic solid, then, according to Voigt, we ought to put for S terms like cr \7 ^U + b^dS f dx. To this Lommel replies*' that the matter molecules each as a whole are not affected by the pas- sage of the wave of light, but that intra-molecular or atomic motions are set up, and that the forces arising from these are represented by his terms, how he does not explain. Of course, since it is assumed that U = Ae'-'^*'"^''"'^'",. V^U= — {h + iy;/c)-U, the difference between the two will only show itself in a change in the refraction formula. The main criticism * of Ketteler's work relates to the method in which the equations are obtained. To this we have already referred. § 10. After these criticisms we turn to the consideration of Voigt's ^ own theory. His fundamental equations are, as we have seen, ' Ketteler, ' Constructionen zur anomalen Dispersion,' ^]'ied. ^1««. t. xi. p. 210; ' Einige Anwendungeii des Dispersionsgesetzes auf duichsichtige, halbdurchsichtige und undurcbsichtige Mittel,' Wied. Ann. t. xii. p. 363 ; ' Experimentale Untersuchung iiber den Zusammenhang zwischen Refraction und Absorption des Lichtes,' Wied. Ann. t. xii. p. 481 ; ' Photometrisclie Untersuchungen,' Wied. Ami. t. xv. p. 336. " ' Bemeikungen zu Herrn Lommel's Theorie des Lichtes,' Wied. ^M7i. t. xvii.p. 468. » Seep. 213. * Lommel, ' Zur Theorie des Lichtes,' Wied. Ann. t. xix. p. 908. ^ Voigt, ' Ueber die Grundgleichungen der optischen Theorie des Herrn E. Ketteler,' Wied. An7i. t. xix. p. 691 ; ' Duplik gegen Herrn Ketteler,' Wied. Ann. t. xxi. p. 534; Ketteler, ' Erwiederung auf Herrn Voigt's Kjitik,' Wied. Aim. t xxi. p. 178;: ' Duplik gegen Herrn Voigt,' Wied. Ann. t. xxii. p. 217. " Voigt, ' Tlieorie des Lichtes fiir vollkommen durchsichtige Median,' Wied. Ann.. t. xix. 13. 873. ON OPTICAL THEORIES. 231 ■ (51) X' and S' are each put equal to zero, and the condition A + A = is assumed ; that is, it is supposed, as we have stated before, that the sphere of action of each ether particle on the matter is small compared with the dimensions of the element of volume considered. An expression is then found for the rate at which work is being done on the compound medium, and the condition formed that this expression should be a function of the time only. So far as the terms depending on the mutual reactions are concerned, the rate of increase of the energy is given by s;=.p(™..)„(A'?(^.B.!0:^).c*^))- + S j d (surface) Afc 8/,^,. = J (vol.) + J (surface) (52) where the S implies that more than one medium may come into con- sideration, and the integrals are to extend over the whole volume of each separate medium and all the interfaces between the media, these being indicated by J (vol.) and J (surf.) respectively. Forms are then found for A, B, C which make J (vol.) a complete differential coefl&cient with respect to the time, and at the same time lead to linear equations of motion which admit of solution in the form u = '^Ae^'-' *'""'*' "~ * '''\ Four possible forms are found, which are given below. (1) - A, = «i(it - U) + 03(1' - V) + 0^(10 - W) /ox A d(v-Y) d(w - W) (2) A,=p, ^ ^^^ ^ -p, ^,^ dt (3) -A, = r, d2(«_U) , d-^iv-Y) d^(iv-W) h ■ (^3) dt^ + s df + S2 dt^ (4) _ d^(v-Y) d^w-W) 23 dt^ df^ It will be noticed that (1) gives us Helmholtz's theory ; (3) gives us Ketteler's in the modified form I have suggested ; for an isotropic medium it is shown that the coefficients and s vanish. Lommel's form is not included in the above ; it is therefore, we see, inconsistent with the conservation of energy in the medium. But there are other terms in the volume integral J (vol.) which will, when combined with suitable terms in the surface integral J (surf.), make the whole up to a differential coefficient of the time. These terms are given by -A = dK dx dij dA, dz (54) 232 EEPOET— 1885. etc., and lead to terms in the volume integral d (volOrA.. -^^(J-^) + A„ i^X!i^) + A. ^^!(!i^U) + . . 1 L dtdx " dtdu ' dtdz ^ • • • I ■= -^ (let us suppose) . (55) Then /' is a function of ^^"~ , etc., and four possible forms are found for A^, etc., viz. putting x, etc., for the difiPerential coefficients dJu-V)^ etc. dx (5) /'j, a homogeneous function of xi . . . X9 -(A,).5 = 'p',etc. Thus — A,, = Em, ,. x , etc., with n^=n^;. (6) -A. = 2^.,% etc., dt with the conditions p,-, = 0, giving /g = constant. (7) -A -Sr ^*X.- with ?-,j = »v,, (8) -A, = ^,,^. with2,.i=0, qu=-qj;, and -/' = SSg,/^- ^'_^ixA We have thus eight possible forms of values for A, etc., all or any of which may occur in the equations. In the equations for the ether, U, V, W, being very small compared with ii, v, w, are omitted. An isotropic body is one in which no one direction differs in its properties from any other. For such a body it is supposed that the forces defined by 2, 4, 6, and 8 above do not exist, and a, a' being the coefficients in -2/'^ and - 2/'^ respectively, it is shown that the equation for plane waves travelling parallel to z is — ON OPTICAL THEORIES. 233 and hence, 1 m{e > + «) e 4aV2 \2 s^ m + r- n\^m 4eir2 X being the wave length in air and N the refractive index. The complete valne for A is — .._/i(^J2,..n^),.*ii=n)_.0.-^) .(57) and in the above equation (56) U has been treated as small compared ■with u. We see that the first and last terms are those given by the theories of Ketteler and Helmholtz respectively ; Voigt's more general theory includes them as particular cases. The first and third terms occur in the theory developed by Boussinesq, which is also included in Voigt's. In a further paper, in reply to some ci-iticismsof Lommel, who argues that a wave propagated through the molecules of the medium must be a BOund-wave, and that therefore the matter motion which affects the trans- mission of light must be i'7?ira-molecular not «(<er-molecular, Voigt shows,' by taking the matter motion into account, that the velocity of wave propagation in a medium constituted as supposed will be given by a quadratic equation. One root of this quadratic will be comparable with the velocity of light in this medium, the other with that of sound ; while the ratio of the energy of the matter to that of the ether in the light- motion is the reciprocal of the same ratio in the sound-motion. Voigt's theory applies only to perfectly transparent media, and its aim is to show that the optical properties of all such media can be explained on an elastic solid theory by considering the mutual reactions of two mutually interpenetrating elastic media. The author does not touch the problem of absorption, because for that purpose we require to deal with the molecular motion to which, in his opinion, heat effects are due, and these lie outside the domain of elastic solid theories. He does, however, deal with double refraction, circular and elliptic polarisation, and the various problems connected with reflexion and refraction. Most of these have been treated of also by Lommel and Ketteler. Chapter II. — Double Refeaction. We will consider first the problem of double refraction. All three explain it in a similar manner. Within a crystal the action of the matter particles on the ether will depend on the direction of vibration, and some or other of the constants of the theory will be functions of this direction. It is assumed that the ether remains isotropic, and that there are three axes of symmetry, which are taken as those of the co-ordinates. § 1. Lommel 2 in his theory treats the constant we have denoted by a^ as a function of the direction, ft'^, which determines the action between ether and matter, and y^, on which the frictional effects depend, ' Voigt, ' Zur Theorie des LicMes,' Wied. Ann. t. xx. p. 144. * Lommel, ' Theorie der Doppelbrechung,' Wied. Ann. t. iv. p. 55. 234 REPORT— 1885. are left invariable, so that the ether equations remain unaltered, and the matter equations become — and similar equations with a^ and a-^. It has been shown by him that for a transparent medium the velocity is given by 1/r, where r is a radius, drawn in the direction of displacement of the surface — - (^^ + 2/^ +^^ - 1) ( ^ti + N;ti + NT^i) =«=^ + 2/^ + ^^ (59) and the directions of vibration are the axes of a section of this surface by the wave. These results are at variance with experiment, which requires that the wave surface should be that of Fresnel, and no reason is assigned in the paper for making a? rather than /3^ or y^ a function of the direction. Circular polarisation and the rotation of the plane of polarisation ' are also treated of by introducing into the equation for U the term — 2/111 cos a-j- , and into the equation for V, 2u2 cos a-- , where I de- dt at pends on the strength of the magnetic force, and a is the angle between its direction and the axis of z. From this it follows that the rotation is proportional to and the results of calculation agree fairly well with Verdet's experiments.* For the rotation of sugar terms of the same kind, but without the cos a, are introduced. It has been shown long since, by Airy,^ Neumann, and MacCuUagh, that such terms in the equations would lead to results in fair agreement with experiment, and Lommel does not attempt any other justification of their existence than that the results they lead to are in agreement with experiment. Similar remarks apply to his paper on the properties of quartz,'* in which the same terms are added to the differential equations already found for a crystalline media. The two waves travelling in any given direction inclined at an angle 6 to the axis are elliptically polarised. The elliptic paths of the particles are similar ; their ratio is given by — ^ 6 8in2 0+ {62 8in<0 + <^o^cos''e]^ ' • ^^' and the difference of phase between the two by ^2 = J2 sin4 a + (^^2 cos" fl . . . (61) where h and dg ^.re functions of the refractive indices and wave lengths. The axial rotation is given by — Q = c i^'-/) ' .... (62) ' Lommel, ' Theorie der Dehnung der Polansationsebene,' Wied. Ann. t. xiv. p. 523. 2 Verdet, Ann. de CUm. (3), t. (59, p. 471. ' Airy, Phil. Mag. June, 1846 ; Neumann, Die mai/netischen Belmnngen, Halle, 1863 ; McCuUagh, Roy. Irish Trans. * Lommel, ' Theorie der elliptischen Doppelbrechung,' Wied. Ann. t. xv. p. 378. ON OPTICAL THEORIES. 235 These results are all in close agreement with experiment. In another paper ' this formula is carried to a higher degree of ap- proximation, and redaces to Q, = -^ — — — ^. This agrees well with the measurements of Soret and Sarasin, between the wave lengths 7604 and 2143. § 2. Ketteler's contributions to the theory of double refraction have been very numerous. Most of the papers already mentioned,- contain something on the subject. The theory given in the first of the papers mentioned is in its fundamental principles in close accordance with that developed by Lord Rayleigh in 1871, though the equations given on p. 95, following Von Lang, as representing the motion in a crystalline elastic solid are incorrect. In it a distinction is drawn between the displace- ment normal to the ray, which leads, it is said, to equations of the form — (m + mj^^+^=a'-^ht . . . (63) at- dx and those in the wave front, for which the equations are — ^"^-■^i^^S) =''-"' ■ ■ ■ (•=*) The arguments by which the second equation is deduced from the first are somewhat obscure ; they are, however, further developed in a later paper.3 The ray direction is defined as that in which the energy of the vibration is propagated, and the direction of vibration is normal to this. The fundamental equations of this theory have already been given.* They are, in their final form,^ . (65) where the constants Cq, /3, k and y may all be functions of the direction. It IS shown in the paper (' Optische Controversen ') now before us that the conditions of incompressibility require that Co, k- and y should be constant, so that the theory turns entirely on the variability with the direction of /3, or rather of C, which is connected with Cq by the equation— C' = ^^.-Co (66) <■ n '^^^^ ^^ ^^*^^ ^° *^® groundwork of the theory, for in its form in the Optische Controversen ' it is assumed that C and Cq are unconnected. 1 he paper ' Zur Dispersionstheorie ' starts wdthout the term in /3, arriving at the equation C + Co=0, and then (p. 208) inserts the /3 ' in ^ ' Lommel, ' Das Gesetz der Eotationsdispersion,' Wied. Ann. t. sx. p. 578. ■• p. 179 ; and also Ketteler, ' Zur Theorie der Doppelbrechung,' Wied. Aim. A t!™; ^; V ' ^^^°"e <^er absorbirenden Anisotropen-Mittel,' MonatsUr. der Konigl. Aitad. der Miss, zu Berlin, November 13, 1879. ! ^etteler, 'Optische Controversen II.' Wied. Ann. t. xviii. p. 631. * See p. 228. * Ketteler, ' Zur Dispersionstheorie des Lichtes,' Wied. Ann. t. sxi. p. 199. 236 BEPORT— 1885. order to explain experimental results.' Introdacing the term C, as defined above, the equations become — (67) These equations will not lead to satisfactory results. Circular ' and elliptic polarisation are also treated of by Ketteler, and are explained on the supposition that terms of the form — Av + %-^\ come into the equation for U, and terms + (l\} + g^") into that for V. The rotation in a magnetic medium is given by ti = ir p ~ ' ^ N being the refractive index, while the value of N in a crystal like quartz may be found from the formula — W-\ = (N,2 _ 1) (1 + cos^fi) + (Na^ _ 1) sin2 « ± [(Nj^ - ■^^^) sin* + 4fc2A2cos2 0(N,2_l)(N,2cos2« + N22sin2<9-l)]'. . (68) Ni and Nj being the refractive indices at right angles to the axis, and A;, a constant on which the rotatory power depends. For ordinary active media the law of the rotation is " = a+^2 + ;^4 + .etc. . . . (69) It will be noticed that in the theories of both Lomrael and Ketteler the rotatory terms are introduced into the equations of the matter particles, and affect the ether only indirectly through the values of «, v, and w. § 3. Voigt's work ^ embraces double refraction and circular polarisa- tion. The existence of three principal axes is assumed, and for these the coefficients o and s in the values of /j and /,* of equations (53) vanish. The values of /^ and/7 are written down with coefficients a^, aj, etc., and a,', tta', etc., respectively, and finally the equation of motion for u is obtained in the form — "*" ^"^ + ^'^ ddy + ^'^ + ^-^J^z "^ £ [similar terms with a/, etc.] (70) It will be seen that there are enough coefficients here to give any imaginable theory of double refraction. Put m + r, = «i,, etc. Then the equations may be written > Ketteler, ' Theorie der circularen und elliptiscben polarisirenden Mittel,' Wied. Ann. t. xvi. p. 86. " ' Theorie des Liclites fiir vollkommen durchsichtige Median,' ]\'ied. Ann. t. xix. P- 873. * See p. 231. ON OPTICAL THEORIES. 237 Where A, = A, + A/— 5, A; and A,' being functions of a, h, c, etc., and P ar cLtt is a linear function of p and the differential coefficients ^-, etc. ax The equations in this form may be compared with Green's, which differ from them only in the facts that his coefficients of drujdt^, cPy /dt"^, and d'^z/dt'^ are the same, and his other coefficients are independent of the time. Voigt's equations, in fact, include both Green's and those given by Lord Rayleigh. Let r be the period of vibration, and denote ?h, — n^T- by Tj, etc. ; then. it is shown that if we assume the relation — + — - + — = 0, in order to ax ay dz obtain Fresnel's wave surface at all the condition T, = T2 = T3 = Tia necessary. These equations being satisfied, the other relations required to give Fresnel's construction on either assumption as to the connection between the plane of polarisation and the direction of vibration are those given by Green, with the addition that since in Voigt's coefficients the period is involved, and since Fresnel'a construction holds for all wave lengths, each of Green's relations splits into two. A difficulty as to the meaning of the constants leads Voigt to prefer Neumann and MacCullagh's theory as to the position of the plane of polarisation. To obtain Fresnel's original construction it is necessaiy to suppose B]2 to be different from B21, and this would imply that elastic reactions are bi'ought into play by rotating an element of ether as a whole without dilatation ; that, in the ordinary notation of elastic solids, T,j^ is different from T,j,. If we treat this as out of the question, then B12 must be equal to B.,], and Fresnel's original construction for the plane of polari- sation is impossible. Circular polarisation is explained by the terms introduced by/2, /4,/g, and/^ of above,' but the terms to which /j and /g would give rise are omitted as not necessary to explain any known phenomena, and the equations in an isotropic medium become — ■ , , .d'^U f , ^dHl, . , d^U , dv , p'dH /^,n^ (.^ + 0^2 = («--),-^+«;p^.-'- + ^^+<7^, • (72). etc. ; the rotation produced by a thickness c of the medium will be — Q.— !V(e + a)(m + r- )V rvJr'^2(e + a)r2J- The same terms are then applied to a crystal, and the case of a uniaxial crystal such as quartz is worked out in full. The equation to determine the velocity in a direction making an angle 6 with the axis is found to be — a and h being the velocities at right angles to the axis. This paper then gives a consistent account of the propagation of light in all known transparent bodies. We proceed to deal with the problem ' See p. 231. 238 REPORT— 1885. of reflexion and refraction on this theory, and after that to make some general remarks on the whole. Chapter III. — Reflexion and Refeaction. § 1. Lommel, so far as I am aware, has not considered the problem of the reflexion and refraction of light on his theory. Ketteler, however, has discussed it in many of his papers. In one of the earlier papers ' the fundamental principles on which he intends to work are laid down. They ai'e as follows : — I. The conservation of energy. Ila. The continuity of the stress pai'allel to the surface of separation. 116. The continuity of the component of the force on an element resolved normal to the surface. III. The continuity of the displacement resolved along the surface. The reasons given for 116. in place of the correct principle of the continuity of the stress normal to the surface are not very clearly stated. No assumption, except such as is implied in I. and III. combined, is made as to the displacement normal to the surface. The principles are then applied to the general problem, but in express- ing them in symbols, except in the case of I., the motion of the matter is entirely neglected. Thus the stress considered in II. is only that arising from the action of the ether ; the part which springs from the reaction of the matter is omitted from consideration. Again, in forming the equations connecting the amplitudes of the incident reflected and refracted rays, 116. is not employed. Ketteler's work, then, in this paper is not really specially connected with his theory of the mutual reaction between the ether and matter. It is rather a modification of Fresnel and Green's work, for which there can be no justification assigned. The problem of metallic reflexion is discussed, and in a second part ^ of the same paper that of moving media. In the next paper on this subject ^ the correct principle of the continuity of the stress normal to the bounding surface is introduced in place of one of the other conditions, but it is supposed that the term involving the dilatation disappears in consequence of the incompressibility of the ether ; in reality, as Green showed, the coefficient of that term is very large, and it must be retained to give correct results. Ketteler fails to see this, and hence concludes that the retention of Green's longitudinal wave is unnecessary. He then considers, as Green had done, the problem of total reflexion ; and, through not taking into account the continuity of the dis- placement normal to the surface, appears to be able to do without the longitudinal waves. The motion of the matter particles does not come into consideration. Another series of surface conditions are given in the next paper on the subject,'* and the matter particles being treated merely as a sort of ' Ketteler, ' Beitrage zur einer endgiiltigen Festst^Uung der Sch-wingungsebene des polarisirten Lichtes,' Wied. Ann. t. i. p. 206. ' Ketteler, Wied. Ann. t. i. p. 5.56. ' Ketteler, ' Zur Theorie der longitudinalen elliptisclien Schwingnngcn im incom- pressiblen Ether,' Wied. Ann. t. iii. pp. 83, 284. See also Theoretisclie Optili, p. 130. •• Ketteler, ' Ueber den Uebergang des Lichtes zwisclien absorbirenden isotropen nnd anisotropen Mitteln und iiber die Mecbanik der Scbwingungen in denselben,' Wied. Ann. t. vii. p. 107. ON OPTICAL THEOEIES. 239 ballast, their motions do not come into the surface conditions. "While, finally,' Ketteler adopts the principle enunciated by Kirchhoff,^ and already discnssed above,^ viz. that no work is done by the action of the stresses in the media on the bounding surface. In applying this principle he equates to zero, as Kirchhoff has done, the terms involving the dilata- tion ; and this, as has been already shovs^n, leads to MacCullagh's formulae on his assumption as to the equality of the density in the two media, and to Fresnel's if the rigidity be assumed equal in the two. The theory is applied to metallic reflexion and total reflexion within crystals in another paper.^ Thus, while Ketteler's first theory ^ was in reality Green's erroneously altered, this second theory is that given by Kirchhoff" in the paper ah'eady quoted. Neither of them really seems to me to involve the distinctive features of Ketteler's theory of the propagation of light. § 2. Voigt's theory is contained in the paper already referred to.^ The conditions assumed are : — I. The displacement of the parallel to the surface ether is continuous in the two media. II. The displacement normal to the surface multiplied by the density is continuous.^ III. Kirchhoff"s principle — viz. that the work done by the stresses on the interface of the two media vanishes. In evaluating the expression for this work Voigt takes into account correctly the terms arising from the action of the matter on the ether. The displacements which come into the equations expressing the first two conditions are strictly displacements of the ether relatively to the matter, but since it is assumed that the motion of the matter particles is very small compared with that of the ether, the absolute displacements of the ether particles are introduced. The results arrived at, however, are hardly satisfactory. In the first place, in evaluating the expression for the work done on the surface, the term involving the dilatation is omitted. Voigt has taken it into account in his equations of motion ; his reason for omitting it here is not given. He thus avoids the question of the so-called longitudinal vibrations. _He then considers the case of vibrations at right angles to the plane of incidence, and arrives at the formulae — E, + R, = D. . (^1 4- r, - ni !-2) (E, - R,) sin^j cos^i ■ . . (74) = (wi2 -t- r.j — «2''^) Dj8in02cos^2 ■ B, R, and D being the amplitudes of the incident reflected and refracted waves. ' ' Ketteler, ' Optische Controversen II.' Wied. Ann. t. xviii p 632 '' Kirchhoff, Ahhandl. der Berl. Ahad. 1876, p. 57. ' See p. 193. * Ketteler, ' Ueber Problems welche die Neumann'sche Eeflexionstheorie nicht losen zu konnen scheint,' Wied. Ann. t. xxii. p. 204. ' See p. 162. « Voigt, ' Theorie des Lichtes fur vollkomnien durchsichtige Median,' Wied. Aim. t. XIX. p. 873. See also Voigt, ' Ueber die Grundgleicbungen der optischen Theorie des Merrn E. Ketteler,' Wied. Aim. t. six. p. 691, especially p. 696 sen. ' See p. 186 ; also Cornu, Ann. de Chim. (4), t. xi. p. 283. 240 EEPOKT— 1885. These become MacCullagh's and Neumann's formulas on the assumption that ???, +ri = ?Ho + r, ) - - . . . . (75) They become Fresnel's if ' ... (76} ' I a\=a for these equations lead — remembering the value of the velocity — to the condition — m^ + ^1 — WjT^ _ sin 2^ 2 m^ + r^ — ^2^^ sin^0, For the vibrations in the plane of incidence the results of the first and second principles are inconsistent with that of the third. For the first and second give (E„ + R^) cos^i = DpCos^)2 ) 771 1 (E^ — R,,) sin ^ 1 = mj D,, sin ^2 > while the first and third give, instead of this second equation, (to, + r, — H., r^) (Ep — Up) sin*! = (wg + ?'2 — "2'') Dp sin02 • (78) They become consistent If Ave assume mi ^7^21 ^^d, adopting Neu- mann's hypothesis, r, = r2. Ml ="2, or, adopting Fresnel's, ei+ai = e2 + a2) ci''i=ct'2- In another paper' it is shown that KirchhoflT's principle, when applied to circularly polarising media, leads to an impossible result, and the principle is modified by the supposition that the work done is a function of the time only, and not zero. The theory of ordinary absorbing media is developed ^ from the supposition that terms involving a loss of energy may come in through the mutual reaction of the ether and matter, and it is shown that these would lead to terms of the form — t — - + cv^-, in the equation for at at u, which merely becomes, for waves travelling parallel to z, where (80) In considering the problem of reflexion in this case, Voigt assumes that the plane xy being the face of incidence, Mtw is continuous. The ' Voigt, ' Das G. KirchhoflE'sche Princip und die Tlieorie der Reflexion und Brechiing an der Grenze circular-polarisender Medien,' Wied. Ann. t. xx. p. 522. ^ Voigt, ' Theorie der absorbirenden isotropen Medien,' Wied. Ann. t. xxiii. p. 104. M. dH dt^ = A, dho — ,du ^d! + ' ^dzm M.= :«l, + '"i - "•1 r A,= = e, -4- «i - a', 72 f ] ON OPTICAL THEORIES. 241 principle laid down in the former paper ' would require that this should be mw, not Mw, as he points out, remarking that the equation given is only true under certain restrictions, and, in fact, he shows that for vibrations in the plane of incidence the continuity of Mw is inconsistent with the energy equation, at least unless & = 0. The energy equation gives M.,w,=^L,w._-h^T^- I . . . (81) and this form is assumed for the rest of the work. Expressions are then found for the difference of phase between the reflected, refracted, and incident beams, and for their relative intensities, and these are compared with theory on the assumption that the con-' stant h vanishes, and that Mj =M2. The results of the comparison are satisfactory; but this, however, can hardly be said for the principles from which they are deduced, while the difficulties we have already alluded to as to the negative value for the real part of the square of the refractive index remain in their full force. Chapter IV. — Theoet of Sir "William Thomson. General Considerations. § 1. The lectures of Sir William Thomson delivered last year at Baltimore have developed a new interest in the theories now under con- sideration. After discussing at some length the elastic solid theory and throwing much light on it, and on the meaning of the twenty-one coefficients of Green's theory, he points out its unfitness to explain the phenomena, and then proceeds to work out the consequences of a special form of reaction between the ether and matter ; this he illustrates in his own inimitable manner by his mechanical model of the ether within a transparent body. This mechanical model consists of a number of concentric hollow spheres. Each sphere is connected with the one withm it by zigzag springs, and in the centre there is a solid mass connected also by springs with the shell next to it. The dimensions of these shells, which represent the matter molecules, are supposed to be small compared with the wave length. The interior molecule will have anumber of periods of vibration depending on the number and nature of the spring connections, on its own mass, and on the masses of the shells. The springs are supposed to be massless. The shell molecules are distributed through the ether in very large numbers, and the outermost shell is connected with the ether. It is further supposed that the forces arising from the springs are proportional to the relative displacements of the centres of the shells, and that the ether acts on the first shell with a force proportional to the relative displacement of that shell and the ether surrounding it, so that, if 4 be the ether displacement, .^,, Xo those of the shells, mJ4,7r'\ m^/47r^, etc. their masses, the equations of motion are, m. 4^2 -^ = <^2 (2^1 - aJa) - C3 i^i - X3) ' Voigt, Wied. Ann. t. six. p. 900. See above, p. 239. looo. (82) E 242 EEPOET— 1885. etc. If we suppose the whole motion to be harmonic and of period t, then the equations become -^f^i = G,{i,-x^)-C^{x,-x^) . . . (83) etc., from which the motion of the various shells can be determined. The system will represent Helmholtz's theory if we suppose the viscous terms in his expression to vanish, and consider only a single shell. The solution in the general case is carried further by putting and ^^._ _ C,x,-, The equations may then be written — u • (84) Wj = tti «2 = ^2 — ^'^ (85) "-s / etc., whence we find Mj as a continued fraction. By differentiating these expressions with reference to t~^, and writing ^ for -, we find — Su, = 7», + (9i±l ] w .^ , + (^i±&A \^^ + , etc. . . (86) Hence J^'=-73^7{-^^^.^ + -.>.-^>l+ • • • •} . . (87) Thus tt decreases as r increases, and if we start from r, a small quan- tity, the us are all large and positive ; hence alternate shells are movincr in opposite directions, and the motion of consecutive shells rapidly decreases. As r increases the ii's decrease, and after a time one will become negative, passing through zero — it can be shown that ttj is the first oije thus to become negative. This gives the first critical case in the solution, for then re, is infinitely great compared with ^, and the solution fails. This equation can be put into the following more convenient form — .^=li{jM^+Ji|!^ + . ...}.. (88) where c,, (C2, etc., are the critical values of r, and R,, Rg, etc., represent the ratio of the energy of the several shells to the whole energy of the system. To apply this to the motion of the ether in a transparent body, let «ii/47r2, etc., represent the whole mass contained within shell No. 1 per unit vol., let p/47r2 be the density, and el^v"^ the rigidity of the ether, aud suppose the first shell, of mass m,, to be connected by a spring to a massless ON OPTICAL THEORIES. 243 spherical lining, which is in rigid connection with the ether outside. Then the equation of motion is — Let the solution of this represent a train of waves of period r and length X, and let V be the wave velocity for the medium. Then and if n be the refractive index, since the velocity in free space is y/ ejfj we have, if we put Ciki^Ri=g',mi, etc. P L + gi-^i^ fe + TT +••••) ~ *®^™^ ^^22, ?3 I . • (91) It follows from this that, ji must be very little less than unity if the formula, neglecting the terms in q^, etc., is to apply to a transparent sub- stance such as rock salt, which gives a value for^ between 1 and 2 for a range of the spectrum from the visible light to the longest waves emitted by a Leslie cube. The formula, we note, is the same in form as that given by Ketteler and Biuot (see above, page 181), and Ketteler has shown that in some fairly transparent substances the coefficient 1 — ^i is appreciable, gi ^s essentially less than unity, so that the term in r^ comes in with a negative coefficient. The formula, then, will explain ordinary ■dispersion fairly if we put q2, 23) ^tc., all zero and take r greater than ki. The critical cases are then discussed from the form In this, r is greater than k\ and less than /cj for ordinary refraction. As r decreases down to k^, jj? passes through the value infinity and then becomes negative, we have greater and greater refraction, and then the waves cease to be transmitted and absorption takes place. And here we are met with the question — What becomes of the energy thus absorbed ? According to our equation the ratio a;, jl becomes infinite, and the solution as it stands fails to meet this difficulty. Helmholtz introduced the term —y'^dJJIdt into the motion of the first shell, and this, representing as it does a viscous consumption of energy by the matter rnolecules, is objected to by Sir Wm. Thomson. Helmholtz's solution given on p. 221 becomes identical with that at present under discussion if we put y=0 ; it is to meet this case in which t-^c, that the term in y* is introduced, for if k represent the co-efficient of absorption on Helmholtz's theory, and we suppose y to be small, then, with Thomson's notation, •v2t< (t* - Ki2)» very approximately, K being a constant, and Jc may be very small except when r is nearly equal to k^. B2 h' 244 EEPOET — 1885. In order to acconnt for the extreme transparency of a substance such as water, we must suppose h to be so exceedingly small that Sir William prefers to consider it as zero, and says : ' I believe that the first effect when light begins, of period exactly equal to c,, is that each sequence of waves throws in some energy into the molecule. That goes on until somehow or other the molecule gets uneasy. It takes m, (owing to its gi-eat density relative to the ether) an enormous quantity of energy before it gets particularly uneasy. It then moves about, and beo-ins to collide with its neighbours, perhaps, and will therefore give you heat in the gas if it be a gaseous molecule. It goes on colliding with other molecules, and in that way imparting its energy to them. This energy is carried away (as heat) by convection, perhaps. Each molecule- set to vibrating in that way becomes a source of light, and we may thus explain the radiation of heat from the molecule after it has been got intO' it by sequences of waves of light.' Helmholtz's equations are, of course, the more general, and apply to- an absorption band as well as to the part of the spectrum for which the medium is transparent. It would seem that the term —y^dU/dt may rightly represent just the effect of that loss of energy in the form of heat due to the irregular collisions of which Sir William speaks, an effect which is only appreciable in the result when, owing to the coincidence of the periods, U tends to become large compared with u, or,, in Thomson's notation, Xi large compared with ^, and in this case x^ will not become infinite, for the amplitude will be multiplied by the factor e-*^', and k being large, the limit of the product comes into consideration. Such a system oF ether with attached matter molecules is thus shown to account for the phenomena of dispersion. A serious difficulty, how- ever, is encountered when we reach the problem of double refraction. §2. For we may suppose, in order to account for it, that C, is a func- tion of the direction, and that for two principal directions it has the- values Ci and C/, while C2 is a constant independent of the direction. Then, with only one enclosed mass, h - Co) ,, = l + C^All ±, .... (93) and to give a dispersion formula resembling Cauchy's we must have 7Hi/-2 considerable compared with C2,_and Ci large compared with either. Hence, if /i' be a second principal index, //2=1 + C and therefore r'^fc — — -^ p (c, + c,-^')(c/ + c.-5-) which, remembering the relative magnitudes of the quantities, and writ- ing Dand D' for the approximate values of the denominators, becomes ON OPTICAL THEOKIES. 245 60 that the difference between the squares of the refractive indices will be inversely proportional to the squares of the wave length, and this is quite contrary to experiment. The question as to whether the theory here suggested would lead to Fresnel's construction is not considered. In a later lecture Sir "William returns again to the question of what becomes of the energy absorbed by the molecules, and of the nature of the ether. As to the latter he adopts Stokes's view, that the medium may be perfectly elastic for the small disturbances of a light-wave, executed, as they are, in the twenty-million-millionth of a second, and yet be a perfect fluid in respect of forces which act, as may be supposed in the kinetic theory of gases, for the one-millionth of a second. Now, the numerical calculations of Professor Morley, undertaken at Sir William's suggestion, show that the energy given to a system such as described tends to become absorbed by the vibrations of lower modes, so that the original energy appears as vibrations in which the period may be the millionth of a second instead of, perhaps, the twenty-million-millionth, and this energy shows itself in the motions which we deal with in the kinetic theory of gases, rapid it may be in themselves, but slow compared with the light- vibrations. § 3. Metallic reflexion and the quasi-metallic reflexion of such sub- stances as give anomalous dispersion are dealt with, and it is shown that the phenomena are such as would be produced by making jx^, a negative quantity, and this is given by values of r a little below the critical period. Thus the molecular explaaation of the great reflecting power of silver is that the highest mode of vibration of the molecules with which silver loads the ether is graver than the mode of the gravest light or radiant heat which has ever been reflected from silver ; and if, again, for certain modes /x^ is not negative, but less than unity, it shows that, conformably with the experiments of Quincke on gold leaves, we should expect light to travel through the medium faster than through air. This forms a marked and most important distinction between this theory and others which have been given to explain metallic reflexion. For the other theories the metallic effects arise from the importance of the viscous terms of the form —ydujdt. In an appendix Sir William works out the problem of reflexion and re- fraction, following Green and Lord Rayleigh so far as ordinary transparent media are concerned. He then transforms Green's formute for vibra- tions in the plane of incidence to the case in which /x^ is a real negative quantity, and arrives at formula expressing, on a strict elastic solid theory, the intensity and change of phase in a wave reflected from metal. According to this solution we have, if v"^ = — fx^ so that v^ is positive, the values of * and ^ given by — * = — >'^ cos (aa!-|-&y + w<) + tan fl!^^*— ^tL_i_ sin {ax + 1]! + ut) *i= — v^cos{ax + hy + ut)—\ja.nd ^^'''^ ' sin ( + aa.' + &y + wQ r^ — 1 . vVj'2 + 1^ , . , \. (95) ^ = - ^^ _^' e-"^ sin (by + wt) 1 ^ ' *' = _ ('-' + !) v'-l bx sin (ly + ut) 246 REPORT— 1885. These are simplified if we put — A2 = ((,.2 + 1) 52 + ,,2^2} r^ + tan B Q^^t^l , 2 = tan/ S = v^ sec/ (96) and the displacements in the transparent medium are then, for the incident wave, and for the reflected. — — S sin (ax + hy + wt +/), A -— S sin (— ax + ly -{■ wt — /). A In this case the rigidities in the two media are supposed to be equal. Sir William has also worked out the problem in the case in which the rigidities are not equal, in the hopes that by this assumption combined with variations in the density — or rather effective density — the variations from Green's formula in the case of light polarised at right angles to the plane of incidence may be accounted for. He finds, however, that, any difference of rigidity which might, combined with a difference of' density, be sufficient to reconcile Green's theory with experiment would cause the proportion of light reflected at normal incidence to be greater than {(/u — l)/(/j + 1)}2, and this value, given by Green's theory, agrees closely with Rood's experiments. We are thus driven back to Lord Rayleigh's case of equal rigidities in the two media. For metals, then, we are to have the rigidities equal, and the value of ^i^ decreasing' from — 00 when r = /.i to zero when r = /.-, /N, N being some lai-ge nume- rical quantity, and then again augmenting from zero to unity as r decreases from kJ'N to 0. ■ The dynamics give no foundation to a theory such as Cauchy's, in which n' is a complex quantity. For light polarised in the plane of inci- dence we have, if n and n be the rigidities, and r = n'/n, ) ... (97) and tan e = i-(i -sec^^^ + tan^ej^j R = i (H- r2(v2sec2 -I- tan^e)} ^ 4 = R cos {ax + by+o)t — e) i . . . (98) ^= R cos (— ax + by + wt + e) ) for the incident and reflected wave ; and for the refracted wave, f = /T^(-^ + ^"'=«^-cos(%-FwO . . . (99) According to these formulaj the reflexion is total from a metal surface at all angles of incidence. Sir John Conroy has recently shown that the loss is exceedingly small. If light be polarised in any plane, then the vibration in the plane of incidence is retarded relatively to that at right angles to that plane by the amount 2f+ 2e — tt. If we suppose v and rv to be both very large numerics, this retardation becomes — ON OPTICAL THEORIES. 247 and from the observations wliicli have been made on the value of the principal incidence, for which the retardation is ^tt, we can find a value for rr. For silver Sir J. Conroy's observations give (rv)~^ = 3'65. And here we are met with a great difficulty. Experiments show that there is very little chromatic eflPect about metallic reflexion. Thus, since the value of the principal incidence depends mainly on ry, this quantity must be independent of the period. Now v^ + 1 is approximately proportional to T^ when r is small compared with Ki, and so this result requires that r, which is proportional to the effective rigidity, should also vary in a certain definite manner, and it is difficult to see how the theory is to give this. The theory is then applied to the case of a thin metal plate, and leads to the fact that the phase of both components is accelerated by the transmission. The accelerations for the two cases are given by — c cos ^+( — — — l^^, vibrations normal to the plane of incidence, d cos 9 + ( T~ — ) \ vibrations in the plane of incidence, V4 Try when S is the thickness of the plate, and e and /are found in the same manner as above. This acceleration was discovered by Quincke, but the details of his results do not agree well with the formulas. The formulas are consistent with Kerr's discovery of the rotation of the plane of polarisation by reflexion from an iron plate when magnetised, but not with Kundt's result that transmission through a thin plate of iron in a magnetic field produces a very large rotation of the plane of polarisation. In a final appendix an account is given of a gyrostatic molecule, the properties of which would give to the medium the heliacal effects seen in sugar and other active solutions. The molecule consists of a spherical shell in which are imbedded two gyrostats having a common axis, which initially is a diameter of the shell. One end of each axis is connected with the shell by a ball-and-socket joint, while the second extremities of each are connected together at the centre of the shell by a second ball- and-socket joint. § 4. Having thus given an account of the various theories proposed based in some way on the mutual reaction between th,e ether and matter, it remains to compare and contrast them. The theories of Boussinesq and Voigt have much in common, and neither of the two as they stand applies to the case of bodies showing strong absorption, for the matter motion is entirely neglected. The theo- ries of Sellmeyer, Helmholtz, and Thomson come under one head in that they all make the mutual reaction to depend on the relative dis- placement of the matter and ether. Lommel's theory seems to me untenable : in its original form it con- tradicts the third law of motion, and if modified so as to be consistent with that, it leads to impossible laws for the relation between refraction and absorption ; besides this, his theory of double refraction does not lead to Fresnel's wave surface, and there seems no reason why the co- efficient a^, which occurs only in the equation of motion of the matter, should be the one to be treated as a function of the direction. The laws of circular polarisation and of the double refraction in quartz, to which the theory leads, and which seem to agree with experiment, may be obtained 248 EEPOKT 1885. with sufficient approximation to fit the experiments from other theories ; and, indeed, the fact that the wave surface in quartz does not become a sphere and a spheroid when the heliacal terms are neglected is fatal. "With regard to Ketteler's theory in the form finally given to it by its author,' it seems to me to have no possible mechanical basis. With the interpretation which he gives of the constants involved, his equations appear to contradict Newton's third law as effectually as do Lommel's, while, so far as the problem of reflexion and refraction is concerned, I cannot recognise the validity of Kirchho0"'s principle as it is applied by Ketteler. At the same time I think that the suggestion of Ketteler — to which, however, he himself takes objection— already mentioned, leads to results which, so far as dispersion is concerned, agree closely with experiment. We may with advantage compare the dispersion formula which it gives with that which comes from the theories of Helmholtz and Thomson. If we neglect the terms depending on viscous action, we have, accord- ing to Helmholtz, for ^, the refractive index, ( \* ^ :1- pXi f""i ^1^ ^-1 (100) while, according to the modified form of Ketteler, f ° 5 '■ 1 + S U2 1— - (101) Ketteler's equations come from Thomson's or Helmholtz's by writing for C, the quantity — 4^20, /r^, or for /j^ in Helmholtz's notation — n^pi^. We may write Ketteler's equation in the form of a series thus — =^l [l+lD{*f + j^;*+ ....}] . (102) two terms of which will give us Cauchy's series with three constants. This modification leads also to an escape from one of the difficulties suggested by Sir William as to the explanation of double refraction. For his general expression for yu^ will become, if we write for Cj the value -4T2Ci/r2, 47r2C, yu2 = l + + •)} (103) If we neglect for a moment the terms on which the dispersion depends, as being small compai-ed with the term 4-Tr^Cilp, which gives rise in the first instance to refraction, we get that 4^r2(Cj-C/) (104) and there will be double refraction independently of the period. ' Ketteler, ' Zur Dispersionstheorie des Lichtes,' Wied. Ann. t. xxi. p. 199. ON OPTICAL THEORIES. 249 It is another question, and one which we shall discuss shortly, whether the double refraction thus produced will give rise to Fresnel's wave surface. There seem, then, to be reasons why we should expect terms such as Ketteler has suggested in our equations — terms which will make the mutual reaction of the ether and the first matter shell depend rather upon their relative accelerations than upon their relative displacements. It is not so €asy to suggest a mechanical connection between the ether and matter which would give rise to this force, but at the same time there is, I think, no mechanical reason to be urged against it. Voigt's theory of wave propagation is in one way more comprehensive than those we have considered, while in another it is less so. It is more romprehensive in that it includes both sets of terms with some others in the expression for the mutual reaction ; it is leas so in that it treats the ratio U/m as a small quantity which may be neglected. This same remark applies to Boussinesq, whose work in one sense is more general that Voigt's, in that he considers the efifect of the attached molecules on the condensational or pressural wave. The presence of these molecules has been shown in Bonssinesq's paper to alter the effective compressibility of the medium as well as its density and its rigidity. In the ether we assume that the compressibility is small compared with the rigidity, so small that the ratio of the two may be neglected, and this must still be the case, even when the ether is loaded. But when dealing with the problem of reflexion we are concerned with the refractive index of the medium for the condensational wave. This will depend on the ratio of the two effective compressibilities, as well as on that of the two effective densities, and though either of the two compressibilities may vanish when compared with the rigidities, in considering their ratio it becomes necessary to take into account any change due to the loading of the ether. It may not be unreasonable, then, to suppose that the effective density of the ether for the condensational wave is different from the effective density for the transverse wave. This supposition would account easily for the variation from Green's formula observed when plane polarised light polarised at right angles to the plane of incidence is reflected from a transparent surface, in that it would allow us to introduce the second constant jjq, as suggested by Haughton and Lord Rayleigh.' Let us now consider Voigt's theory. With regard to the problem of reflexion his surface conditions appear to be unsound. The ether is the continuous medium, and the surface conditions must apply to it simply. The conditions of continuity demand that the actual displacements of the ether and the actual stresses over the interface, arising, of course, in part from the action of the matter, should be the same in the two media. The validity of Kirchhoff's principle has already been considered, and it has been shown that it does not lead to results in accordance with experi- ment, for it does not give the change of phase which in some cases accompanies reflexion. But, while this is so, Voigt's theory shows us that the effects of the attached molecules may show themselves either in the rigidity or the •density of the ether. Now, the work of Lord Rayleigh and Lorenz has proved that the effects of reflexion are due mainly, if not entirely, to differences of effective density ; and so we must look to the terms in ' See p. 192. 250 BEPOET — 1885. Voigt's theory whicli aflPect the density as the most important. These terms are _(,g,+ „)(„-U). The other terms, show themselves as a variation of the effective rigidity. In order to obtain a consistent theory of reflexion we must treat these as of secondary importance compared with the first terms. Now, this is inconsistent with both theories of double refi-action as advanced by Voigt, for the first condition for either is that r and n must be independent of the direction. It would seem from this that they should be the same in all media. Boussinesq adopts the opposite view. He makes his double refraction depend on the terms which correspond to r and n, and neglects the variations of the others with the direction. If we do this — and we seem to be forced into it by the further requirements of our theory — the funda- mental equations in a crystal become those given by Lord Rayleigh. These, we have seen, if we assume the strict transversality of the vibrations, do not lead to Fresnel's wave surface. On the other hand, if we suppose that the vibrations in a crystal are at right angles to the ray, not to the wave normal, the result agrees with all the consequences of experiment, for we obtain Fresnel's surface as the wave surface, but we are left in a difficulty as to the normal wave. With regard to metallic reflexion, the theory as given by Sir "W. Thomson explains completely the difficulty raised by Lord Rayleigh as to a negative value for ^^. It does not, however, enable us to decide how much of the effect is due to the fact that the highest possible free period of the ether in the metallic medium is below that of the incident light, and how much is due to opacity arising from terms such as dujdty&s supposed by Lord Rayleigh. The correct equations to which such a theory would give rise are yet unsolved, but the principles required by the solution are well known. It seems, then, that this theory promises to afford us the solution of the difficulties which still surround theoretical optics, and to account at once for the phenomena of reflexion and refraction, dispersion and double refraction. Of course, in all cases of transparency the matter motion is infinitesimally small compared with that of the ether. The ether is to be looked upon as moving through a sort of network of fixed matter particles. Terms depending on the reaction between the ether and these fixed portions of matter will be introduced into the equations, and these terms will be expressible as functions of u, v, w and their differential coefficients. The matter particles will not move appreciably, and their movement is not necessary for the explanation of refraction and ordinary dispersion ; for on Ketteler's modified theory we have, if we omit the viscous terms, in rrifx (»'''* — «,*)' and the ratio of the amplitudes is /32n2 fi(^v'^ — n'^) ON OPTICAL THEORIES. 251 From the value of /i^ we see that y3^ must be comparable with m, the density of the ether, so that, except when «^/(»2 — ?t^) is a large quantity, the ratio of the amplitudes will be inversely as the densities, for l^^/fj will be comparable with mjij. When, however, n-j{_v^ — ii^) is large, the matter motion becomes appreciable, and the phenomena of anomalous dispersion arise. Part IV. THE ELECTRO-MAGNETIC THEORY. Chapter I. — Maxwell's Theory. § 1. There remains now for consideration Maxwell's electro-magnetic theory. The fundamental equations of this theory are purely electrical, and are established on electrical principles. According to Maxwell, when electromotive force acts on a dielectric medium the change of condition known as electric displacement is produced. The two are connected by the equations — P = ^/, etc (1) P, Q, R being the components of the E.M.F. and /, g, h of the dis- placement. K is the inductive capacity. In a crystal the equation holds only for the principal axes, and along these K has three diiferent values. The rate of variation of the displacement given by/, g, h constitutes the current in the medium, and it is an essential part of the theory that — df do dh — + — + d.e dy dz vanishes everywhere. The current is connected with the components of the magnetic in- duction a, b, c by the equations — de dh . J ._, etc., and the magnetic force a, /3, y is given by a = fici (3) etc., where /i is the coefiBcient of magnetic capacity. a, b, c are also given in terms of a quantity known as the vector potential, the components of which are F, G. H, by the equations — fZH dG ''=dy~^ ^^^ etc., and from these it follows that W=|^-V2F .... (5) etc., where j_ dF ^ dB. dx dij dz 252 EEPOET — 1885. while the electromotive force at any point is also determined in terms of this same quantity F, G, H by the equations p_ dF d^ , etc., ^[' being the electrostatic potential. From this it follows that ,K^(^+f)-v^F+.f-=0 .... (7) dt \ dt dx J ax etc., and the vector F travels through the medium with velocity 1/n/K^. Now, the value of this quantity can be determined by experiment, and agrees very closely indeed with the velocity of light. Thus the vector potential, and in the same way the electric displacement and the magnetic induction, travel through the medium with a velocity, as nearly as we can eay, identical with that of light. Moreover, the electric displacement corresponding to this is in the wave front, and the same is the case with the magnetic induction a, h, c. By this motion energy is conveyed through the medium, the electrostatic energy depending on the electric displacement, the electro-kinetic on the magnetic induction, and the two can be shown to be equal. Thus the theory agrees with the undulatory theory of light in assuming the exist- ence of a medium capable of becoming a receptacle of two forms of energy. Electric displacement and magnetic induction are, then, changes of condition which can be propagated in waves of transverse disturb- ances through the medium with a velocity practically identical with that of light. Maxwell's theory supposes that there is an intimate connection between the vibrations which constitute light and electric displacement ; according to some of his followers the two are identical, though, so far as I can judge, that is not necessary to the theory as he left it. Now, experiment shows that the value of /j. is nearly the same for all media, so that it follows that on this theory the specific inductive capa- city of a medium — the ratio of its inductive capacity to that of air — should be equal to the square of the refractive index. Experiments have shown that while this law is by no means true for all substances, it is suffi- ciently nearly so for many to render it probable that V K gives the most important term of the index. In estimating the value of the comparisons we must remember that while K is determined by observations lasting over an appreciable time, the refractive index depends on vibrations of great frequency ; to compare the two, then, we have to adopt some dispersion formula, and find the value of the index for waves of infinite period, and this alone is a source of error. Again, the equations for a crystalline medium are obtained by Maxwell, and he shows that the velocity of wave propagation is given by Fresnel's construction, while the electric displacement is in the wave front, and its direction is that of the axis of the ellipse which determines the velocity. The theory is not burdened with a wave of normal vibrations, and accounts quite simply for all the phenomena of double refraction. § 2. The theory of reflexion and refraction of electro-magnetic waves was first given by H. A. Lorentz,' who follows a method of attacking the ' Lorentz, SMomilch. Zeitschrift, t. xxii. ON OPTICAL THEOEIES. 253 problem which is dae to Helmholfcz.' This we shall consider later. It was also solved by J. J. Thomson,^ so far as the isotropic media are concerned, and by Fitzgerald. ^ Some further developments of the theory are given in a paper by the author of this report, and read before the Cambridge Philosophical Society.* In this paper the general equations for the displacement and for the magnetic induction in a crystal are given. If a, b, c be the principal velocities given by the equation 2 1 3tc., then dt^ •' dx\ dx dy dz J ^ ' etc., while d'^n, -J (i^a TO d^a -^ d^a — i. ("a"^" +62^+0^^^ . . . (9) dx\dx dy dz ) ' If a wave of electric displacement S', in a direction in which the inductive capacity is K', be traversing the medium, the electromotive force is 4!7rS'/K' in the direction of displacement, and 4rrS' tan x/^' along the wave normal, when x is the angle between the ray and the wave normal. § 3. The surface conditions implied by the theory, and used by Lorentz, J. J. Thomson, Fitzgerald, and Glazebrook, are that the electric and magnetic displacements normal to the interface are continuous, while the electric and magnetic forces in the interface are also continuous. The formulae obtained are identical with those given by MacCuUagh and Neumann, electric displacement being substituted for the ordinary displacement of the medium. The theory has the very great advantage over the ordinary elastic solid theory that reflexion and double refraction are both explained by variations in the same property of the medium, viz. the inductive capacity. Variations in its value from medium to medium give rise to reflexion and refraction ; variations in different directions within the same medium are the cause of double refraction. § 4. The theory has been applied by Lord Rayleigh to account for the various phenomena ^ connected with the scattering of light by a cloud of small particles. These are deduced satisfactorily from the theory on the supposition that \i, the magnetic capacity, is a constant through the two media, and that the effects are due to variations in the inductive capacity, while, when terms of the second order in A K/K are included, the scattered light does not vanish — the incident light being plane polarised — in a direc- ' Helmholtz, Sorchardfs Journal, Band Ixxii. "^ J. J. Thomson, Phil. Mag. April, 1880. » Fitzgerald, Phil. Trans. 1881. ■• Glazebrook, Proc. Camh. Phil. Soc. vol. iv. p. 155. ' Lord Rayleigh, ' On the Electro-magnetic Theory of Light,' Phil. Mag. Aug, 1881. 254 EEPORT — 1885. tion normal to the incident light, but in one inclined at an obtuse angle to that in which the light is travelling. Tyndall observed this effect when the particles scattering the light cease to be very small. Chapter II. — Hei.mholtz's Theory. § 1. Helmholtz looks at the problem of the propagation of an electro-macrnetic disturbance in a somewhat different manner, and a com- parison of the two theories is given by the author of this Report.' | The electro-magnetic effects in the medium depend, according to I Maxwell, on the values of F, G, H, the components of the vector potential, | or as Maxwell also calls it, of the electro-kinetic momentum, and if we integrate round a closed curve, the values of F, G, H satisfy the equation [Fdx + Gdy-B.dz = {{'^ dsda . . . (10) where ds is an element of the curve, i the current at any point at a distance r from ds, da an element of the curve in which the current i is running, £ the angle between (7s and da, and the integration on the right extends round the two carves s and a. From this we can show that And if we put we find that -4fli dx'dy'dz' +^ dx 4^ + ^+^'=l-v2* dx dij dz 4- V 2F — — - = — 47r/i/ + fi dx dxdt lb r ^dF ^db ,dB. M Helmholtz, starting from the equation f Ydx + Gdy + B.dz = ff '""^' ds da, invest! gates^the most general form which F, G, H can have. He shows that we must write for - ^ of equation (11) the value -Ml^*^,"-''- • • • ("> where fc is an unknown constant. Hence v'F = -W+.(l-'O-0, . . . (W) and by comparing this with (13) we see that 3=-Hk^ (16) dt ' Glazebrook, Proc. Camh. PhU. Soc. vol. vi. pt. ii. See also J. J. Thomson, ■' Report on Electrical Theories ' p. 133 oE this volume. ON OPTICAL THEORIES. 255 If it be necessary that J should vanish, then Z; or — mnst be zero. dt According to Helmholfcz, however, J is not necessarily zero, and the equation to determine it is — ^&k|J=a^J (17) so that J, and therefore *, is propagated through the medium as a wave of normal disturbance with the velocity 1 «uK On Helmholtz's theory there may therefore be a normal wave in addition to the transverse wave. Helmholtz's theory becomes Maxwell's if we put * = 0, and then unless the value Z; = oo is admissible J = 0, and there is no normal wave. If Z; = there will still be no normal wave for its velocity will be infinite. When we consider the problem of double refraction, we can show that all the possible directions of vibration L, M, N corresponding to a given wave normal I, m, n are given by the equation — ■ E (^' - ^' + M ('" -'^') + I ^^"- ^') = • • (IS) There are therefore, in general, an infinite number of such directions. If, however, we are to assume that there are only two, and those the two given by Fresnel's theory, we must have IL + wiM + nTS = 0. Thus Maxwell's solenoidal condition, ^+'ll+f=Q .... (]9) ax dy dz ^ ' is a necessary and sufficient condition to give Fresnel's construction. Chapter III. — Dispersion, etc. According to the theory as left by Maxwell, waves of all lengths travel at the same rate. Dispersion does not come into consideration. This question has been dealt with by Willard Gibbs • and H. A. Lorentz.^ § 1. According to Gibbs's views the displacements of which we are cognisant in the phenomena of light are the average displacements taken through a space which is small in comparison with the wave length, but contains many molecules of the body. The real displacement at each point of such an elementary space probably differs considerably from the average value, and a complete theory should take into account the two. This is done in Gibbs's paper- The average displacements being I, r), ^, the complete displacement is taken as ^ + ^', &c. I', r,', ^' are denoted' as the irregular parts of the displacements. It is shown that i\ r]', C are linear functions of ^, 77, i; ; they are therefore of the same period, and the phase of the irregular displacement throughout the element Dv is the ' J. W. Gibbs, American Journal of Science, vol. xxii. April, 1882. ' H. A. Lorentz, Wied. Ann. t. ix.; Schlomilch. ZeiUcUrift, t. xxiii. 256 EEPOET — 1885. same as that of tlie regular or average displacement, but the relations between ^, ??, ^ and H , r\' , C change rapidly as we pass from point to point of the element. The velocity of wave propagation is found by equating the maximum potential and kinetic energies of the medium. It is shown that the equations lead to Fresnel's consti-uction in the case of a crystal if the solenoidal condition be assumed, while the relation between f.i the refractive index and \ the wave length is given by 1 _ H 2w,H.' y^--2-Kk'^ x^ .... (^u> H, l\ and H' being constants. The objection which Briot made to Cauchy's theory of dispersion may be made to this. We should expect dispersion in a vacuum as well as in ordinary transparent media. The properties of circularly polarising media are discussed in a second paper,' in which I', r/', ^' are treated as linear functions of s, jy, ^ and their differential co-efficients ; and in a third paper the fundamental equations are re-established in rather a more general form than that given by Maxwell. The generality is gained partly by dealing with the average values of the various quantities, and partly by supposing that the relation between the E.M.F. and displacement is given by [E] = [tj] + >// [U] : . . . (21) ^ and </' being two arbitrary functions, and [ ] indicating that the average value is taken. In the simple theory ^ is a constant, and equal to 47r/K, and -^ zero, and this will not give dispersion. There seems, however, to be no reason — as has been pointed out by Professor Fitzgerald — against applying to the oscillations of the electro- magnetic field the methods and reasoning developed in the third part of this report. Almost the whole of the woi'k can be translated into the lano-uage of the electro-magnetic theory at once. Periodic electric dis- placement in the ether will produce periodic electric displacement in the matter, and the relations between the two will depend on the ratio of the period of the ether vibrations to the possible free periods of the electric oscillations in the matter molecules ; and it is not difiicult to see how the action between the two might depend on the relative electrical displace- ments and their differential coefficionts. § 2. MaxwelP has given a theory of the magnetic rotation of the plane of polarisation on this theory. He assumes (1) that the effect of mag- netic force is to set up molecular vortices in the medium ; (2) that the components of the magnetic force obey the same law as the components of the strength of a vortex in hydrodynamics; and (3) that there arises in the value for the kinetic energy of the medium a term of the form 2C(awi + /3w2 + ywj), w,, W2, ^3 being the components of the angular velocity, and a , /3, y of the magnetic force. For the case of waves travelling parallel to z the kinetic energy is shown to be T = i^>(^2 + f,^ + i-^) + cy(.) g - ig) . . (22) ' J. W. Gibbs, American Journal of Science, vol. xxiii. June, 1882. « Maxwell, Electricity and Magnetism, vol. ii. p. 40. ON OPTICAL THEOKIES. 257 and tlie equations of motion, From this it follows that the rotation per unit length is fl = „„,;l(i_x|) .... (24) where i is the index of refraction, and this formula agrees well with experiment. It should be noticed that in obtaining this formula Maxwell deals with the displacements of an ordinary medium ; the forces assnnied are those arising from the elastic reactions of this medium, the vortex motion in which is connected with the magnetic force. The displacements are not treated as identical with the electric displacements, nor is any indi- cation given of the connection between the two. § 3. Fitzgerald, in the paper already mentioned, applies the theory to the case of reflexion from a magnetic medium. He finds that when plane polarised light is reflected directly from such a medium, the reflected light is slightly elliptically polarised. This is not in accordance with Kerr's experimental result, but Fitzgerald treats the iron as a trans- parent, or nearly transparent, substance with a real refractive index. § 4. It was shown by E. H. Hall that when a current passes across a conductor in a magnetic field an electromotive force is produced whose strength is proportional to the product of the current and the strength of the field, and whose direction is at right angles to the plane containing the current and the field. By introducing into the equations for the electromotive force terms expressing this, so that they become ^=-%-^-^{yg-fth) .... (25) at p etc., Prof. Rowland ' has calculated the magnetic rotation of the vectors F, G, H, and, on the assumption that a similar efiect will be produced in a dielectric, arrives at the same formula as that given by Maxwell. § 5. The main difBculty of the theory, and the one which stands most in the way of its general acceptance, is the diSiculty of forming a clear phy- sical idea of what electric displacement is, and various analogies have been suggested with a view to rendering the difficulty less serious. One of these, due to Helmholtz,^ is developed in a paper on the molecular vortex theory of electro-magnetic action.^ It is shown there that, if the components of the magnetic force be identified with the molecular rotations in a con- tinuous medium in which the displacements are s, v, C, then the compo- nents of the electro-kinetic momentum are equal to J^^l, etc. ; and the equations of the electrical field in a conductor would imply that the medium in the conductor has the properties of a viscous fluid, while in a dielectric, so far as the motion to which the undulatory effects are due is ' Eowland, Phil. Mag. April, 1881. - Helmholtz, Crelle Journal, t. Ixxii. ^ Glazebrook, Phil. Mag. June, 1881. 1885. a 258 KEPOET — 1885. concerned, its properties are those of an elastic solid in which the elec- trical displacement / is given by ^'/=-v^'+i(|4;40 . . . w The objection that it is impossible to maintain a continuous molecular rotation in an elastic solid may be made to this analogy. It seems, how- ever, possible that, as suggested by Professor Stokes when considering the problem of aberration, the ether may behave as a perfect fluid for all motions involving more than a very small relative displacement of its parts, while for such small displacements as are contemplated in the theory of light it has, in a dielectric, an appreciable rigidity. In a con- ductor the effects of this rigidity, if it exist, are masked by the more powerful effects of the viscosity. The fluid is no longer perfect. Chapter IV. — Rowland's Theory of the Peopaqation of Plane Waves. § 1. The propagation of waves of electro-magnetic disturbance from a given source has been recently very fully considered by Professor Rowland,' and we proceed to give some account of his paper. Rowland considers very generally the solution of the equations — ^=V2v2F, (27) etc., and allied equations given by the system F. + , ='^'--^' .... (28) so that F, G, H satisfy the solenoidal condition. He puts ^_(,„+i) being a spherical harmonic, and C„ a function of p. He finds ^^+2(a-i6)^?a.-JiOM:l)c,.=0 dfj^ dp p^ whence f nn+1 n{n'^-l'') (n+2) C„-Co|l-^-^ +-^^5 ^" + - • where c = a — ib. He then takes, as a special solution, etc., and treats the case of symmetry round the axis of x, for which ^ _ (- i)"Q.- i p"n! Q„_, being a zonal harmonic with the axis of x for axis. ' Rowland, American Joxi/rnal of Mathematics ; Phil. Mag, June, 1884:. • (29) •} (30) . (31) • (32) ON OPTICAL THEOEIES. 259 Let be tlie angle between this direction and that to the point at which the disturbance is required, p the distance to the point, and a the angle between the plane xOp and some fixed plane. Let 0', 9" denote disturbances perpendicular to the radius vector in the plane xOp, P' P" along the radius vector, and N' N" normal to the wave plane xOp. Then it follows that if we have small electric displacements X'e~'*'^~^'" parallel to x throughout the small sphere (fTrR' = dv), that e' = - 2^0+^2 gX' ^.^ Q^_ a^-vn^,, \ L/Q b-p P'= ^3!^'cos0e-'^O'-V'>(Zi; | ' Co 4Tp2 ) N' = 0" = P" = j^„^3&^X^sin0C,^_,,,,_v„^ 1 .... (34) 0, = 0.(1-^1) 3i 3^^• • • ■ (35) where C,= - ^° G - 4~by) This agrees with the results given by Stokes and Lord Rayleigh, already quoted,' N" being proportional to the rotation. The effect of a general arbitrary electric and magnetic displacement is then found. In considering the optical problem it is pointed out that electric displacement is always accompanied by magnetic, and that the effects of the two must be considered, and according to the views of Professor Rowland the two must be considered independently. From the relation between the electrostatic and electromagnetic energy, it follows that if there be an electric displacement X'e*^' there will be a magnetic Y"e'"'' where Y" = ^X'. The electric displacement at any other point of space is found and expressed as below. Let the origin be the point at which X', Y" act ; the axis of z the normal to the plane of X'aY" ; p the direction in which the effect — at a point A — is required ; the angle 2OA = d, and the angle between zOA and zOx = ^ ; and let P', 0', 4>' be the displacements along OA, and normal to 6 and f. Then e' ='!pT cos <p [a + COS d)(l -i] - e^l e-':^o.-vo ^ 8'^P ^[_^ -T ^\^ j^; ^2^2]^^ [-(36) P'= ^4^8in0cos9.ri_lV'^^-v« 47rp2 r ^ ^^j ' See p. 201. 82 260 EEPOET — 1885. And we can show that in the value of 6' it is the 1 in (1 + cos 0) which comes from the assumed magnetic disturbance, while in <S>' it is the cos d in the same term. The magnetic disturbance produces no effect in the value of P' . Neglect- ing the magnetic disturbance we arrive at Stokes's result for the effect of a disturbance X'e''^'* on the medium, which is used by Rayleigh in the paper on the blue of the sky. Now we may note that the result of the experiments on scattered light seems to disprove this hypothesis of Rowland's as to the necessity of considering the two disturbances, for according to him the intensity is the same at all points in the plane xy at the same distance from O. This is not true ; the intensity varies as sin^a if a is the angular distance of the point from the axis of x. Again, it is true, of course, that the magnetic disturbance accompanies the electric, but it accompanies itas a consequence. If we produce, by some impressed force, a varialale electric displacement at a point in the medium, and calculate the effect due to this, we have done all that is necessary. There will, it is true, be magnetic displace- ment, but it can be calculated from the electric. Rowland's results do not apply to the case of a wave being propa- gated through an aperture, for in this case we have no right to assume that the disturbance produced by an element is symmetrical round the direction of vibration . We have not a single particle or an indefi- nitely small sphere vibrating and sending out its effects in spherical waves ; we have a state of motion coming in from behind the aperture, and being continually propagated across it at a given point P and at time to, we must consider the circumstances at any point O of the aperture at a time t^ such that OP = &(i — fo)- For these will be the initial circumstances so far as we are concerned ; and at this time t^, has an initial velocity and an initial displacement, Both these require to be considered in dealing with the question, and we have to adopt Stokes's' method of solution, and we again arrive at his theorems with regard to the relation between the direction of vibration and the direction of diffraction. § 2. The electro-magnetic theory, if we accept its fundamental hypo- theses, is thus seen to be capable of explaining in a fairly satisfactory manner most of the known phenomena of optics. The great difficulty is, as we have said, to account for the properties which the medium must have in order to sustain electrical stresses. These consist in an electrostatic field of a hydrostatic pressure KR^/Stt, combined with a tension KR^/47r along the lines of force ; R being the resultant electrical force, and K the inductive capacity. There will therefore be a difference of pressure in different directions in the ether. Combined with this difficulty there is another of a similar kind, that of realising mechanically what electric displacement is, of forming for oneself a physical idea of a change of structure in some medium of unknown properties which shall obey the laws implied by the various equations satisfied by the components of electrical displacement. Optical effects are certainly due to changes, periodic in space and I time, of some properties of a medium which we call the ether. Electro- magnetic effects are also due to variations in properties — it may be the same as those which give rise to light — of the same ether. When the ' On this point reference has already been made, see p. 206. ON OPTICAL THEOEIES. 261 electro-magnetic effects become rapidly periodic they travel -with the velocity of light, and the direction to which the change of property is related is in the wave front, at least for isotropic media. The rigidity or quasi-rigidity through which the medium has the power of propagating these transverse waves of small displacement may be given to it through other motions which are going on independently of the light. The free passage of the planets through space proves that it can have little if any viscosity or rigidity, though, according to the views of Professor Stokes, while behaving as a perfect fluid for all appreciable motions, it might conceivably be rigid for the very small displacements in a light-wave. Taking Sir W. Thomson's estimate of the density of the ether as about 10"^- grammes per cubic centimetre, the rigidity required for the propagation of light would be about 10""^ The rigidity of glass is about 2-5 X 10". While it might, then, be conceivable that the ether should have this very small rigidity and yet ofier no appreciable resistance to the earth's motion, it is difficult to reconcile this with its power of standing electric stress, and we are forced to con- clude that the change implied in electric displacement is much more than a mechanical displacement of the molecules of a perfect fluid. A qnasi-rigidity might be conferred on the fluid by filling it with vortices, and it might thus become capable of conveying transverse waves and of standing electric stress. Electric and magnetic polarisation would then consist in definite arrangements of the vortex rings or filaments. Changes in these arrangements, or in some of the properties connected with them, would constitute electric and magnetic displacements, and possibly also h'ght. We should then have a complete electro-magnetic theory of optics, or rather a complete theory of the ether embracing electro-magnetism and optics, but towards this theory our present knowledge has made only a small advance. Report of the Committee, consisting of Professors Ramsay, Tilden, Marshall, and W. L. GtGODwin (Secretary), appointed for the purpose of investigating certain Physical Constants of Solution, especially the Expansion of Saline Sohdions. TocR Committee have to report as follows : They have obtained apparatus for determining the rates of expansion of saline solutions fi-om -20° C. to -f60° C. They have devised experiments for determining the distribution of a weighed quantity of water between molecular weights of two salts, the three substances being placed in separate vessels in the same enclosed space kept at a constant temperature. But further progress in either of these directions was interrupted by the continued illness of one of the Committee. Your Committee respectfully ask for reappointment. 262 EEPORT— 1885. Third Report of the Committee, consisting 0/ Professors Williamson, Dewae, Frankland, Crum Brown, Odling, and Armstrong, Drs. Hugo Muller, F. E. Japp, and H. Forster Morley, and Messrs. A. Gr. Vernon Harcourt, C. E. G-roves, J. Millar Thomson, H. B. Dixon (Secretary), and V. H. Veley, reap- pointed for the purpose of dratuing up a statement of the varieties of Chemical Names ^vhich have come into use, for indicating the causes tvhich have led to their adoption, and for considering what can he done to bring about some conver- gence of the views on Cheriiical Nomenclature obtaining among English and foreign chem,ists. An account of tlie authorship of some of the various systems of nomen- clature which have been devised for the purpose of distinguishing between compounds formed by the union of the same elements in different propor- tions, has been given in the ' Historical Notes ' prefixed to the Second Report of this Committee. Among these systems the use of the termina- tions oMs and ic, to denote respectively lower or higher degrees of saturation of one element or group with another element or group, is perhaps that which has met with the widest acceptance. This system further directs that when electro-negative groups, the names of which end in ous and ic, unite with electro-positive groups to form salts, these terminations are to be changed into ite and ate respectively. Before proceeding to discuss the practical application of this system, it may bo well to point out, as a minor etymological detail, that the literal meaning of the terminations ous and ic has altered since they were first employed. Thus ous (Latin osus) ought to denote, on the part of the compound, richness in that element to the name of which the termination is attached. For example, cujirous (cuprosus) means ' rich in copper ' : cuprous oxide is primarily an oxide which is richer in copper than cupric oxide, and only by implication an oxide which is poorer in oxygen. This implied signification is, however, that in which the name cuprous oxide is nowadays employed. A curious result of this change of literal meaning is to be found in the use of the prefix hypo to denote a still lower degree of saturation than that expressed by ous. Thus the name hyponitrous acid is taken to denote an acid containing still less oxygen than nitrous acid ; whereas hyponitrous really means ' less rich in nitrogen,' which is the vdty opposite. Had the etymology been logically carried out, the prefix ought to have been hyper. A similar confusion of ideas is displayed in the use of the prefixes hyper and per at the other end of the scale ; in place of these, hypo ought to have been employed. Ferchromic acid does not, as its name literally taken signifies, contain more chromium than chromic acid : it contains less, and ought consequently to have been termed /typo-chromic acid. It need hardly be said that it would be ill-advised to attempt to change a system so firmly established as that involved in the present use of these prefixes hypo and hypier ; and in the above remarks on the etymology of the subject, nothing of the kind is intended. No ambiguity can arise from the use of terms about the meaning of which everyone is agreed, and their mere etymological accuracy is, in view of this all-important consideration, of secondary importance. ON CHEMICAL NOMENCLATUBE. 263 The following list will show the application of the ic and ous nomen- ilature to salts and salifiable oxides : — I. List of Salts where Two or more Series of Compounds are formed.^ Name denoting metallic Formula of corre- Name denoting metallic Formula of corre- radical of salt sponding oxide radical of salt sponding oxide Cuprous Cu.O Chromous CrO Cupric Cub Chromic Cr„03 Mercurous Hg,0 Uranous u6„ Mercuric HgO Uranic ( tJranylic) UO3" Aureus Au„0 Manganous MnO Auric Au„03 Manganic Mn,03 Thallous Tlo'O Ferrous Feb Thallic TLO3 Ferric Fe,03 Stannous Snb Cobaltous CoO Stannic SnO„ Cobaltic Co„03 Cerous CeoO'a Platinous PtO Ceric Ceb„ Platinic PtO^ Names corresponding with ijlatinous and platinic would be applied to the corresponding oxides and salts of the other metals of the platinum gi'oup — distinguishing, however, the other oxides and salts of this group by numeral or other designations. The designations given in this Table to the various higher and lower series of salts and salifiable oxides have been employed with almost complete uniformity by all chemists who have adopted this system of nomenclature. As a metal rarely — if ever — forms more than two salifiable oxides, the ous and ic terminations generally suffice for purposes of distinction so far as the salts of metals are concerned. The practice of further employing these terminations in the case of acid-forming oxides does not lead to confusion, since these oxides are distinguished by the name anhydride (or acid). CrO Cr^Og Chromous oxide. Thus we have Cr03 Chromic oxide. Chromic anhydride (Chromic acid.) Indifferent oxides have frequently been classified and named by regarding them as compounds of salifiable, with acid-forming oxides, CrjO^ being termed chromic chromate. For stages lower than ous, the prefixes hi/po and sub are employed. Custom appears to have restricted hypo chiefly to acids and to acid-forming oxides, suh to salifiable and to indifferent oxides. With regard to the termination o^is, the minor question arises, how far this termination ought to be written in the forms ious and ecus. The answer is : as seldom as possible. ' Cupreous ' has generally given way to ' cuprous ' ; no one writes ' chromious ' (although the name of the metal is ' chromium ') ; and there is no reason why such names as ' ruthenious ' and ' iridious ' should not equally be shorn of their super- fluous penultimate syllable. A further question, concerning which considerable difference of opinion has prevailed, is whether any ous or ic terminations ought to be employed in the names of salts of which only one class is known — thus magnesic sulphate instead of magnesium sulphate. There is something to ' In this list the term ' salt ' is taken to include ' haloid salts,' but to exclude the halogen compounds of those elements whose oxides do not yield oxy-salts with acids, 264 . EEPORT — 1885. be said here for both systems ; and, as the diversity of practice does not lead to confusion, and conseqnently does but little harm (beyond in each case offending the ears of those accustomed to the opposite system), the ques- tion need not be regarded as a vital one. Objections which have been urged against the use of any termination in such cases are that chemists have not always been able to agree as to which termination is to be used in a given case, and that, apart fi"om this, the practice causes beginners erroneously to surmise the existence of a second series of salts. The objection on the other side is that the omission of the terminal ' ic ' breaks the uniformity of the system and leads beginners to suppose that barium sulphate, for instance, has a different constitution from cupric sulphate. In the case of carbon compounds, on the other hand, there is a distinct advantage in aflSxing ic to the names of the positive radicals in ethereal salts. A neglect of this precaution leads to ambiguity — at all events in the spolcen name. Thus, though tliere is no ambiguity in the name etlujl loTienijlacetate when written, yet the ear cannot distinguish between it and etlujlpTienyl acetate. This ambiguity is obviated by the use of the termi- nation ic : thus, eilnjlic plienylacetate and efJiylphenylic acetate. In the use of the terminations ous and ic to distinguish different series of acids and acid-forming oxides, the practice of chemists has also been very uniform. Indeed, with the exception of one or two isolated cases almost perfect unanimity has prevailed. To sum up, the ous and ic terminations when employed for purposes of distinction in cases where two series of oxides, acids, salts, &c., are known, have been almost free from ambiguity, and for this reason deserve to be retained. On the other hand, in cases where only one series is known, those chemists who have employed one or other of these terminations have occasionally differed as to which ought to be used : the difficulty may be solved, as it has been done by some chemists, by avoiding the use of any termination in such cases. In complex cases where the above modes of naming prove inadequate, recourse may be had to numeral designations. These appear especially admissible in cases where an oxide occurs which is intermediate between the ous and ic stage, and at the same time cannot be classed as a com- pound of oxides already classified and named. In applying numeral designations, it is most important to select only such as are free from hypothesis and which afford correct information. In this respect, chemists appear of late years not to have been sufficiently careful. As an example, arsenious oxide may be quoted ; this compound is frequently termed 'arsenic trioxide,' the formula being written AsgOj, and it is tacitly assumed that the molecule contains three oxygen atoms. There are three objections to this name: — (1) That, assuming the formula on which it is based to be correct, it affords no information as to the number of arsenic atoms associated with the three oxygen atoms ; (2) that it involves the assumption that arsenious oxide does not vary in molecular weight, whatever its physical state ; and (3) that the formula of gaseous arsenious oxide is AS4O6. In employing numeral designations to indicate molecular composi- tion in cases where this is established, it is therefore important to express the number of atoms of each constituent element, as dicarhon hexachloride, C2 Clg. But in the case of solid and liquid bodies of which the molecular weight is either unknown or may vary with temperature, the name should indicate merely the relative proportions in which the constituents are associated ; or, more explicitly, the name should indicate the proper- ON CHEMICAL NOMENCLATURE. 265 tion of the radical associated with what may be termed the characteristic element of the compound. No difficulty occurs in the case of the chlorides, or analogous compounds with the monad elements generally, these being termed mono-, di-, tri-, tetra-, penta-, or hexa-chloride, &c., according as combination is in the proportion of 1, 2, 3, 4, 5, or 6 atoms of chlorine to 1 atom of the characteristic element. The application of this system would involve the use of the names tin dichloride and iron trichloride (not sesqui-chloride) for stannous and ferric chlorides respectively, names which accurately express the relative proportions of chlorine to metal in these compounds without any hypothesis as to their molecular composition — a composition, which in the case of the former compound, at all events, certainly depends on temperature. It will, however, involve a slight depar- ture from the existing practice when applied to oxides, sulphides, and other compounds of polyad elements ; thus oxides of the type (R2)"0 would be termed hemi-o-K.ides, since they consist of the characteristic element and oxygen in the proportion of one atom of the former to half an atom. of the latter. Oxides of the type (R2)"03 would be termed sesqui- oxides, since the characteristic element and oxygen are present in the proportion of one of the former to one and a half of the latter. Oxides of the type R2 O5 would be termed sesterti-oxides, as they contain oxygen and the characteristic element in the proportion of two and a half atoms of the former to one of the latter. Oxides of the types RO, RO2, RO3, and RO4, would be termed respectively mono-, di-, tri-, and <e<r-oxides. Acid Salts. There are two distinct classes of salts to which this name has been given : — 1. Salts with two or more metals, one of the metals being hydrogen. 2. Salts formed from these by the removal of water. Until comparatively lately, no attempt was made to give distinctive names to these two classes, except that sometimes the words hydratic and anhydrous were used to distinguish them. The distinctive names — pyrophosphate, metaphosphate — which Graham gave to the two sets of anhydrous acid phosphates were founded on the supposition that the phosphoric acid (PO5) existed in them in two modifications, different from the acid of the ordinary phosphates. The nomenclature used by nearly all chemists from the beginning of this century until about 1860 is illustrated on tables 3-6. Acid salts in which for the same quantity of base there is 2, 3, . . . &c. times as much acid as there is in the normal salt are called hi ate, ter ate, &c. (in German, doppelt (or zweifach) saures Salz, dreiiach saures Salz, &c.) In English and French the Latin adverbial numerals his or hi, ter, &c. seem always to have been used until about twenty years ago, when Greek adverbial numerals were introduced for the anhydrous acid salts. Watts's Dictionary and Naquet are the first English and French authorities in which we have observed this change. Basic Salts. There are two distinct classes of salts to which this name has been given : — 1. Salts with two or more salt radicals, one of the salt radicals being hydroxyl. 2. Salts formed from these by the removal of water. 266 KEPOET— 1885. These were not distinguished by name until quite recently, and are still very often confused. The nomenclature in general use is illustrated on tables 8-12. Basic salts of oxygen acids in which for the same quantity of base there is ^, ^, &c. as much acid as there is in the normal salt are called di ate, tri (or tris) ate, &c. (in German, halb saures Salz, drittel saures Salz, &c.) Basic salts of oxygen acid were also named by the proportion of base to acid, the proportion in the normal salt being taken as unity — bibasic, terbasic, &c. salts (in German, zweifach, dreifach, etc. basische Salze). Thus ^rt'snitrate (drittel saures salpetersaures Salz) is the same as terhasic nitrate (dreifach basisches salpetersaures Salz), Latin adverbial numerals being used for multiples, and Greek adverbial numerals for submultiples. The compounds of basic oxides with haloid salts (corresponding to the basic salts of the oxygen acids) are variously named ; thus, oxy- chloride, bisoxychloride, basic chloride, bibasic chloride. The numerals here refer not to the number of atoms of oxygen and halogen, but to the proportion of metal combined with oxygen and halogen respectively (or perhaps more correctly to the proportion of equivalents of oxygen and halogen) ; thus 2PbO.PbC]2 is bisoxychloride, or bibasic chloride. It is to be noted that corresponding basic haloid and oxygen salts have not the same numeral ; as — PbO.PbClo is basic chloride (einfach basisches Chlorid). PbO.Pb(N03)9 is bibasic nitrate (zweifach basisches Salz), because it is 2PbO.]Sr20g. 2PbO.PbCl2 is bibasic chloride (zweifach basisches Chlorid). 2PbO.Pb(N03)o is terbasic nitrate (dreifach basisches Salz), because it is SPbO.NgOs- Sulphur Salts. — Table 14. These have sometimes, especially in German, been named as double sulphides, but usually, in Latin, English, French, and recently also in German, follow the names of the corresponding oxygen salts. Sulphur Basic Salts. — Table 1 3. Compounds of normal salts with sulphides of the metal. These were discovered by H. Rose, and called by Berzelius sulphur basic (schwefel basisch), as corresponding to the compounds of normal salts with the basic oxide. This nomenclature has not been generally adopted, and, as will be seen from the table, there is little uniformity in naming these substances. Double Salts. With very few exceptions, these may be classified in two sets. 1. With a common salt radical. 2. With a common metal. 1. With a common salt radical. Here again there are two kinds, (a) Salts of polybasic acids. (6) Compounds of two haloid salts, or of a haloid salt, with a compound of a halogen and a non- metallic element. (a) These are named consistently with the names of the simple salts j as phosphate of magnesia and ammonia, phosphorsaure ammoniak- magnesia, magnesium ammonium orthophosphate, ammonic magnesio phosphate, or, with what may perhaps be called an adverbial modification of the first adjective, ammonio-magnesic phosphate. (h) Of these we may take as examples 2KF, Sir4 ; 2KC1, PtCl4 ; 2KCN, Pt(CN)2; KF, BF3 ; KCl, AuClg ; 4KCN, Fe(CN)2 ; 3(KCN), Fe(CN)3. See Tables 15, 16, 17. ON CHEMICAL NOMENCLATURE. 267 These have been named on three different principles : — (a) As double fluorides, chlorides, etc. ; for instance, fluoride of silicon and potassium, fluorkieselkalium. T!^T (fi) As compounds of the positive metal with a compound salt radi- cal ; for instance, ferrocyanide of potassium, silicofluoride of potassium, kieselflu orkalium . (7) As analogues of oxygen salts ; for instance, fluosilicate of potassium, potassium fluosilicate, potassium chlorplatinate, chloraurate, cyanaurate. The third system seems only to be used when there is really a corre- sponding: oxygen compound. 2. With a common metal. As a well-known substance mentioned by most systematic writers, emerald green has been selected — table 18. It will be seen that where a name is given, it is either acetate and arsenite, or a combined name, acetoarsenite, or arsenigessigsaures Salz. List of Authorities referred to hy their nurribers in, thefolloioing tables. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Author Thomson . . Thomson . . Thomson . . Brande . . . Thomson . . Brande . . . Ongren (Table to Berzelius) Brande .... Graham . . . Gmelin .... Liebig (Geiger) . Mitscherlich . Handworterbuch Kopp's Geschichte (vol. iv.) Kane Graham . . . . Eegnault . . . . Fownes Otto Edition Date No. 20 II. 1804 IV. 1810 21 V. 1817 22 I. 1819 23 vir. 1831 IV. 1837 24 IV. 1838 25 26 V. 1841 27 I. 1842 28 IV. 1843-4 29 V. 1843 30 IV. 1844 I. & II. 1848-64 31 — 1847 32 II. 1849 33 II. 18.50 & 1858 34 III. 1851 35 V. 1854 36 III. 1855-60 Author Miller Eegnault . . . . Rose (French) . . Watts's Dictionary and Supplements Naquet .... Eose (Finkener) Fownes . . . Williamson . . Wurtz's Dictionary Bloxam .... Eegnault Strecker- Wislicenus Kolbe, Kurzes Lebr- buch Fownes Miller Eoscoe and Schor- lemmer Frankland and Japp Kolbe (Humpidge). Edition Date I. 1856 V. 1859 — 1862 — 1863-81 II. 1867 VI. 1867-71 X. 1868 II. 1868 — 1869-76 II. 1872 IX. 1877 — 1877-8 XII. 1877 VI. 1878 — 1878-81 _ 1884 " 1884 1. Muriat of lime. 2. Muriate of lime. 3. Chloride of calcium (also muriate of lime). 4. Chloride of calcium. 5. Chloride of calcium. 6. Chloride of calcium (cal + C). 7. Chloretiim calcicum (CaCl). 8. Chloride of calcium or muriate of lime (Cal+C). 9. Chloride of calcium (CaCl). 10. Chlorcalcium (CaCl). 11. Chlorcalcium (calcium chloratum) (CaCl,). 12. Chlorcalcium (CaCl). 13. Calciumchlorid, chlorcalcium (Salz- saurer Kalk) (CaCi), 1859. 14. Chlorcalcium. 15. Chloride of calcium (CaCl+6Aq). 16. Chloride of calcium (CaCl). 17. Cblorure de calcium (CaCl). 18. Chloride of calcium (CaCl). 19. Chlorcalcium (CaCl). Chloride of calcium. Chlorure de calcium (CaCl). 20. 21. 22. 23. 24. 25. Chloride of calcium (CaCL). S upp . C alciu m cliloride . Chlorure de calcium. Chlorcalcium. 2nd 268 REPORT — 1885. 26. Calcium chloride (CaClj). 27. Calcic chloride (CljCa). 28. Chlorure de calcium. 29. Chloride of calcium (CaClj). 30. Chlorcalcium (CaCL). 31. Chlorcalcium (Ca"Cl2). 32. Calcium chloride (CaCl,). 1. Sulphat of soda. 2. Sulphate of soda. 3. Sulphate of soda. 4. Sulphate of soda. 5. Sulphate of soda. 6. Sulphate of soda (S + .s')- 7. Sulphas natricus (Na S) 8. — 9. Sulphate of soda (NaO,S03+ lOHO). 10. Einfach schwefelsaures Natron. 11. Schwefelsaures Natron (natrum sulphuricum) (NaO,S03,10Aq). 12. Schwefelsaures Natron (NaS + lOAq). 13. Schwefelsaures Natron, neutrales, 1859. 14. Schwef(;lsaures Natron. 15. Sulphate of soda (NaO.SOa + lOAq). 16. Sulphate of soda (NaO.SOa). 17. Sulfate de soude (NaO,S03). 18. Sulphate of soda (NaO.SOa). 19. Schwefelsaures Natron (NaOjSOj). 20. Sulphate of soda (NaO.SO,). 21. Sulfate de soude (NaO.SOj). 33. Calcic chloride (or chloride of cal- cium) (CaCU). 34. Calcium chloride (chloride of cal- cium) (CaCl.,). 35. Calcic chloride (CaCU). 36. Calcium chloride (CaClj). n. 22. — 23. Normal or neutral sulphate of sodium. 2nd Supp. sodium sul- phate (Na.SOJ. 24. Sulfate neutre de soude. 25. Schwefelsaures Natron. 26. Sodium sidphate (SO^Naj) 27. Sodic sulphate (Na.SOJ. 28. Sulfate neutre de sodium. 29. Sulphate of soda (NajO.SOj). 30. Neutrales schwefelsaures Natrium, Oder Dinatriumsulfat (Na^SO^, lOH^O). 31. Schwefelsaures Natron, neutrales 32. Sodium sulphate. 33. Sodic sulphate, or sulphate of sodium (Na^SOj). 34. Normal sodium sulphate (also sul- 1 phate of soda). 35. Sodic sulphate (SOjNaOj). 36. Sodium sulphate. III. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. Supersulphate of soda. Bisulphate of soda. Bisulphate of soda. Bisulphate of soda. Bisulphate of soda. Bisulphate of soda. Bisulphate of soda 0,S0,). (H0,S03 + Na Saures (od. doppelt) schwefelsaures Natron (NaO,2S03 + Aq). Schwefelsaures Natron und schwefel- saures Wasser, zweifach schwefel- saures Natron (NaS- + 3H = NaS + HS + 2H). Schwefelsaures Natron, zweifach saures, wasserhaltendes Salz (NaO,S03 + HO,S03). Saures schwefelsaures Natron. Bisulphate of soda (NaO,S03 + HO, SO3). Bisulphate of soda (HO.SOs + NaO, SO3). Bisulfatede soude (NaO.SO^-t- HO.SO' + 2H0). 18. Bisulphate of soda (NaO.SOa + HO, SO3 + 3H0). 19. Zweifach schwefelsaures Natron, Wasserhaltiges (NaO,S03 + HO, SO3). 20. Bisulphate of soda (NaO,HO,2SO,'). 21. Bisulfate de soude (NaO.SO» + H0. S0» + 2H0). 22. Bisulphate de soude. 23. Hydro-monosodic sulphate (hy- drated bisulphate of soda) (NaH SO,). 24. Bisulfate de soude. 25. Saures schwefelsaures Natron. 26. Sodium and hydrogen sulphate, or acid sodium sulphate (2S04NaH. 3OH2, or SO,Na2.SO,H,.30H2). 27. Hj'drosodic sulphate (NaHSOj). 28. Sulfate acide de sodium (SO^NaH). 29. Bisulphate of soda (Na20,H20,2S03). 30. Mononatrium Sulfat, oder halbge- siittigtes saures schwefelsaures Natrium. 31. Saures schwefelsaures Natron fONa S0„10H 32. Sodium and hydrogen sulphate, 01* acid sodium sulphate (see 26). , S3. Hydric sodic sulphate (acid sul-j ON CHEMICAL NOMENCLATURE. 269 pliate of sodium or bisulphate of soda) (NaHSO^). 34. Hydi-ogen sodium sulphate (NaH SOJ. 35. Hydric sodic sulphate (SO^HoNao). 36. Acidsodium sulphate S0„ f {qm ") IV. 1. 2. 3. 4. 5. 6. 7. 8. 9. iio. 11. I 12. I 13. ' 14. 15. 16. 17. 18. 19. See Table III. Anhydrous bisulphate of soda (S + 2s')- Bisulphas iiatricus Na iS.^. Anhydrous bisulphate of soda (S + 2s'). Zweifach schwefelsaures Natron (NaO, 2SO3). Saures (doppelt) schwefelsaures Na- tron, das wasserleere Salz. Schwefelsaures Natron, zweifach saures wasserfreies Salz. (Not specially named.) Anhydjous bisulphate (a true bisul- phate). Un veritable bisulphate (Na0.2S03). Anhydrous bisulphate of soda (NaO, 2.SO3). Zweifach schwefelsaures Natron, wasserfreies Salz (NaO,2S03), 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. Bisulphate of soda, the anhydrous salt. Un veritable bisulphate (Na0.2S0'). Anhydrosulphate of sodium or an- hydrous bisulphate of sodium (Na„S.,0. = Na„S0„S03 = Na„0, 2SO3) 1875. Disulfate de sonde. Anhydro bisulphate (S0,Na„,S03). Sodic disulphate (NaoS^O,).' Anhydrosulfate. Neutrales Kalium Pyrosulfat. Dischwefelsaures Natron /^/SO,ONa\ \^ \,SO.,ONaj Pyrosulphate (NajSoO, or Na„SO,, SO3). Sodic pyrosulphate (Na^S^O,). Sodium disulphate (Na.SJO,). Sodic pyrosulphate (S^O^NaOo). Sodium disulphate (0{«ggNa^J V. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. (Alkaline chromats.) Chromate of potash [red colour]. Bichromate of ijotash. (Not distinguished from chromates.) Bichromate of potash. Bichi-omate of potassa (2Chr' + P). Bichromas kalicus (KCro). Bichromate of potassa (2Chr' + P). Bichromate of potash (KO,2Cr03). Not mentioned. >> >> Zweifach chromsaures Kali. Doppeltsaures od. rothes chrom- saures Kali (KO,2Cr03), 1859. Bichi-omate of potash (KO + 2Cr03). Bichromate of potash (KO,2Cr03), _ 1858. Bichromate de potasse. Bichromate of potassa (KO,2CrOg). Zweifach od. rothes chromsaures Kali (KaO,2Cr03). Bichromate of potash (KO,2Cr03). Bichromate de potasse. Acid chromate of potassium, di- chromate of potassium, or bi- chromate of potash (K„0.2Cr03 - K2CrOj,Cr03), 1863. Potassium dichromate (K20.2Cr03), 1872. 24. Dichromate de potasse. 25. Saures chromsaures Kali. 26. Potassium bichromate or anhydro- chromate (2Cr03,K.O, or CrO.K,, CrOg). 27. Potassic dichromate (K„Cr,0,). 28. Bichromate de potasse (K„0,2Cr03). 29. Bichromate of potash (K„0,2Cr03). 30. Kalium dichromat. 31. (Neutrales) Dichromsaures Kali. /f. (CrO,OK\ \^ lCrO„OKj- 32. Potassium bichromate or anhydro- chromate (2Cr03,KoO, or CrO.K,, Cr03). 33. Potassic dichromate, pyrochromate, or anhydrochromate (K„0,2Cr03, or KXr^O,). 34. Potassium dichromate, or bichromate of potash (KoCr^O,). ' ' / (CrO^Ko N 35. Dipotassic dichromate (JO ) \ (CrO„Ko / 36. Potassium dichromate. 270 REPORT 1885. VI. 1. — 2. — 3. — i. — 5. — 6. — 7. — 8. — 9. Terchromate of potash (KO.SCrOj). 10. — 11. — 12 13 14. 15. 16. 17. 18. 19. 20. 21. 22. Dreifach chromsaures Kali. Dreifach chromsaures Kali (KO, SCrO^). Terchromate of potash (KO.SCrOs) [1858]. Dreifach chromsaures Kali (KaO, SCrOj). Terchromate of potash (KO.SCrOj). 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. Hyperacid chromate or trichro- l mate of potassium (K„0,3CrOs or K2Cr04.2Cr03 [1803], po- tassium trichromate (K20,3Cr03) [1872]. Potassium trichromate (3Cr03,K,0, or CrO^K„,2Cr03) Terchromate of potash (KjO.SCrOj), Kalium trichromat. Potassium trichromate (3Cr03,K,0, or CrO.,K„,2Cr03). Potassic trichromate (K„0,3Cr03). Potassium trichromate (K^CrjO,,,). 'CrOaKo 35. Dipotassic trichromate 36. VII. 1. 2. 3. 4. 5. 6. 7. 8. 10. 11. 12. 13. 14. 15. 16. 17. 18. Bichromate of chloride of potas- sium. Bichromate of chloride of potas- sium. Bichromate of chloride of potassium (KCl-(-2Cr03). Chromsaure und Chlorkalium (KGl -i- 2 Cr). Zweifach chromsaure Chlorkalium, chlorchromsaure Kali (KGl,2Cr03 Oder KO,Cr03.CrO„ei oder 3(K0. Cr03) + (CrGl3.2Cr03). (KCl, + 2Cr03). Bichromate of chloride of potassium (KCl + 2Cr03). Bichromate de chlorure de potassium, or chlorochromate de potasse (KC1.2CrO='). 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. Zweifach chromsaures Chlorkalium (KaCl,2Cr03). Bichromate of chloride of potassium (KCl,2Cr03). Bichromate de chlorure de potas- sium, or chlorochromate de potasse. Chromochloride of potassium, 1863. Potassium chromatochloride, 1872. Potassium chlorochromate, 1875 L and 1879 (KCl,Cr03). Bichromate de chlorure de potassium. 31. Chlorchromsaures Kali 32. 33. 34. 35. 36. (crO^Sl). Bichromate of chloride of potassium, or potassic chlorochromate (KCl, Cr03?). Potassium chlorochromate (KCrOjCl). Potassium chlorchromate. vni. 1. Nitrat of lead. 2. Nitrate of lead. 3. Subnitrate of lead. 4. Subnitrate of lead. 5. Dinitrate of lead. 6. Dinitrate of lead (2PL -i- n'). 7. Nitras biplumbicus (Pb^isfj. ON CHEMICAL NOMENCLATUEE. 271 8. 9. 10. 11. 12. 13. 14. .16. 16. 17. 18. 19. 20. 21. 22. Dinitrate of lead ((2PL + n'). Bibasic nitrate of lead (PbO,N05 + PbO). Basisch salpetersaures Bleioxyd (Pb-^). Zweifach basisch salpetersaures Bleioxyd (2PbO,5f05, or 2PbO, NO3.HO). Basic salt, containing two atoms of oxide of lead united to one of nitric acid. Bibasic nitrate of lead (PbO,N05 + PbO). Sous-azotate de plomb ; azotate bi- basique (2PbO.N05+ HO). Basic nitrate. Halbsaures Salz (PbO.HO.PbO.NOj). Dinitrate of lead (2PbO,N05). (See 17). 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. Basic nitrates of lead ; diplumbic nitrate. Azotate basique de plomb Basic nitrate. Plumbic hydronitrate (PbNOaHO). Azotate diplombique (Az03)„Pb,PbO or parazotate, (Az20,)Pb2, or orthoazotate (AzOi)"'Pb"H'. Halbgesattigt hydratisch basisch Salpetersauresblei. Basisches Salz r^y^jOjPbY Basic nitrate. Dibasic plumbic nitrate (Pb2N0,, PbHoO„). Basic nitrate, Pb(N03)0H. Plumbic nitrate hydrate, NO, (OPb"Ho). Basic salt. rx. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. Submuriat of lead. Submuriate of lead. Submuriate of lead. Oxychloride of lead. Bibasic chloride of lead (PbCl + 2PbO), Tribasic (PbCl + 3PbO). Einfach-, zweifach-, &c. basisches Chlorblei (PbCl + PbO), &c. Oxychloride of lead. Oxychlorure. Basische Bleichloride, Oxychlorid, Bisoxychlorid, &c. (PbO.PbCl, 2PbO,PbCl, &c.) 20, 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. Oxychlorides of lead (PbO,PbCl, &c.) Oxychlorure. Oxychlorides (Pb^Cl^O or PbCLPbO, &c.), 1881, III. Supp. Oxychlorures de plomb. Oxychlorides PbCL.PbO, &c.) Basic plumbic chlorides (Pb.,OCL, Fhfifi].,., &c.) Oxychlorides of lead (PbCL.PbO, &c.) Diplumboxydchloriir ; Triplumb- dioxydchloriir, &c. Basische Salze. Oxychlorides (PbCl2,PbO, &c.) Oxychlorides of lead (PbO.PbCl,, &c.) Basic chlorides (PbClj + PbO, kc.) Oxychlorides. Oxy- or basic chloride. X. Subnitrate of bismuth. Subnitrate of bismuth. Tetartonitrate of bismuth. Hydrated subnitrate of bismuth. Hydrated subnitrate of bismuth. Subnitrate of bismuth (HO.NO. + 3BiO). 10. Salpetersaures Wismuthoxyd, ein- fach. Basisch salpetersaures Wis- muthoxyd (Bi03,N05-(-Aq). 11. Basisch salpetersaures Wismuth- oxyd ; Bismuthum Subnitricum (NA.BiO + 3Bi0,Aq.N,0.,Bi0 + 2Bi0). 12. Verbindung von salpetersaurem Wis- muthoxyd mit Wismuthoxydhy- drat (BiN + SBiS). 272 REPOET 1885. 13. Basisch salpetersaures Wismuthoxyd, drittelsaures salpetersam-es Wis- muthoxyd. 14. Basisch salpetersaures Wismuth. 15. A basic salt (BiOa + NOj). 16. Subnitrate of bismuth (BiOa.NO^ + H0). 17. Sous-azotate de bismuth. 18. Basic nitrate of teroxide of bismuth (Bi03,N05 + 2HO). 19. Drittelsaures Salz (BiOa.NO^ + 2H0), Bisoxynitrat (2(Bi03,3HO)Bi03,3N05). Subnitrate of bismuth (9HO,4N05, + SBiOa). Sous-azotate de bismuth. 20. 21. 22. 23. 24. 25. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 9. 10, A basic nitrate (BiNO^.H^O or Bi„03,NA.2H,0). Sous-azotate. 26. Basic nitrate (Bi„03,N„05,20H„, or Bi" (N03)3,Bio03',30H;). 27. — 28. Azotate basique de bismuth (Bi'" (AzO,) + H,0 or (BiO) AzO, + H„0). 29. Basic nitrate of bismuth, also called trisnitrate of bismuth (Bi^Oj, NA.H.O). 30. Wismuthnitrat. Bi(0N0„)(0H)2. 31. Basisches salpetersaures Wismuth- oxyd T^jj^logBi or NOjOBiO + H..0). 32. Basic nitrate (see 26). 33. Bismuthous subnitrate (Bi„03, 2HNO3). 34. Basic bismuth nitrate, Bi (OH)^ NO3. 35. Bismuthous nitrate dihydrate, NOj (Bi"H020). 36. Basic bismuth nitrate, Bi(OH)2N03. XI. A subsalt. A compound of with chloride. oxide of bismuth (See 6.) A subsalt (BiCl -1- 2 BiO -1- HO) Wismuthoxyd - chlorwismuth. Wis- muthoxychloriir. Basisch salz- saures Wismuthoxyd (BiClj, 2Bi03). Basisches Salz. (BiCl + 2BiH). Wismuth Bisoxychlorid. Zweifach- basisches Wismuth Chlorid (Bi„ei0j Oder Bi^eia + BiA)- Oxychloride of bismuth (BiCla + 2Bi03 + 3HO). Oxychloride of bismuth (BiCl3, 2Bi03). Oxychlorure de bismuth (Bi.,Cl3 + 2(Bi„03 + 3H0). Oxysulphat of mercury. Suboxysulphate of mercury. Neutral persulphate of mercury. Suboxysulphate of mercury. Disulphate of mercury. A sub-salt. A sub-salt. (HgO.S03 + 2HgO). Schwefelsaures Quecksilberoxyd, Drittel (SHgO.SOj). XII. 19. Bisoxychlorid, zweifach basisches Salz (2Bi03,BiCl3). 20. Oxychloride of bismuth (BiClj, 2Bi03). 21 (See 17.) 22 — 23. Oxychloride of bismuth (BiOCl), 1863. Bismuthyl chloride (BiOCl), 1879. Supp. III. 24. Oxychlorure (BiOCl). 25. Basisches Chlorwismuth. 26. Oxychloride (BiClO). 27. Bismuth oxychloride (BiOCl). 28. Oxychlorure de bismuth (BiOCl or Bi.,03,BiCl3). 29. Oxychloride of bismuth, 2(BiCl3, Bi203),H„0. 30. Wismuthoxychloriir. 31. Basisches Chlorwismuth, Wismuth- oxycblorid (BiOCl). 32. Oxychloride (BiClO). 33. Bismuthous oxychloride, 2(BiCl3 Bi,,03),0H„ or BiOCl. 34. Bismuth oxychloride (BiOCl). 35. Bismuthous oxychloride (BiOCl). 36. Basic bismuth chloride. (Bismuth oxychloride.) 1 1 . Basisches schwefelsaures Quecksilber- oxyd (SHgO.SOa). 12. Basisches schwefelsaures Quecksilber- oxyd. 13. Basisch schwefelsaures Quecksilber- oxyd (3HgO.S03). 14. Basisches schwefelsaures Queck- silberoxyd. 15. Basic sulphate (3HgO + SO3). 16. Sub-sulphate. ] 7. Sel basique (3HgO.S03). ON CHEMICAL NOMENCLATURE. 273 '.SO3). 18. A basic salt (SRgO.SOj). 19. Drittelsaures Salz (3HgO.£ 20. A sub-salt (SHgO.SO,). 21. Sel basique (SHgO.SO'). 22. — 23. Basic sulphate of mercury (SHgO.SOj = HgSO,.2HgO). 24. Sel basique 25. — 26. A basic salt (SHgO.SOj). 27. A basic salt (HgjSOs). 28. Sulfate trimercurique(SOjHg,2HgO). 29. A basic sulphate (HgO.SO3.2HgO). 30. Drittelgesattigtes Mercuridsulfat. 31. Basisches Salz(SOj02Hg + 2HgO). 32. A basic salt (3HgO.S03). 33. A basic salt (HgS04.2HgO). 31. A basic salt (Hg3S06). „ 35. Trimercuric sulphate (SHgOj). 36. Basic sulphate (SOj.OjHg + 2HgO). 10. 11. 12. 13. 14. 15, 16, 17, xm. 18. 19. Chlorosulphuret of mercury (hg + 2C)-i-2(hg + 2S). Chloride and sulphuret of mercury (HgCl + 2HgS). C h 1 o r q u ecksilber- Schwef elquecksil- ber, Oder Chlor- und Schwefel- quecksilber (2HgS,HgCl). SchwefelbasischesQuecksilberchlorid (Berzelius' nomenclature) (HgClj + 2HgS). Quecksilberschwefelchlorid (Hg€}, + 2HgS). Chlorosulphuret (HgCl + 2HgS). Sulphochloride of mercury (HgCl, 2HgS). HgCl + 2HgS, 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. Quecksilbers ul p huretochlorid (Quecksilber chlorosulphuret) (2HgS,HgCI). (See No. 17.) Sulphochloride of mercury (Hg.S, cy. Mercuric sulphochloride (HgjSjClj). Sulfochlorure mercurique C2HeS, HgCL). Chlorosulphide of mercury (HgCl~ 2HgS). Mercuridthiochloriir. (2HgS,HgCl,). Trimercuric disulpho- /HgClrr \ dichloride VHgCl^s^ 36. — 1. 2. 3, 4. 5. 6, 7. 8. 9. 10. 11, 12. 13. 14, 15. 16. Sulphoantimoniate. Sulphostibias natricus (Na Sb2). FiinfEachschwefelantimonnatrium, Antimon persulphid-Natriimi ( S ulpho- stibias natricus cum aqua) (Sb^Sj, NaS + 12Aq) . Natrium antimon Sulphid (3 NaS + SbSJ. Antimonpersulphid-Natrium. Anti- monpersulphid - schwefelnatrium, &c., &c. (Sb^Sj.NaS). Sulphantimoniate (3NaS.SbS.), 1885. XIV. 17. 18, 19, 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. Sulfantimoniate de sulfure Sodium (3NaS.Sb2S3). de Natrium sulphantimoniat (3NaS, SbSj). Sulphantimoniate of sodium (3NaS, SbS,). Sulfantimoniate de sulfure de sodium (SNaS.SbjSJ Sulphantimonate of sodium (NaaSbS- or 3Na2S.Sb2S5). Sulphantimoniates (Sb^S^SMoS or SbS^M,). Sodic sulphantimoniate (SbS^Naj). Sulfo-antimoniate de sodium (SbS. Na3). Sulphantimoniate. Natriumthioantimonat (Na,SbSJ, 274 REPORT— 1885. 31. SbS^Naa, or (SbS) SaNa,. 32. Sodium- sulphantimonate. 33. Trisodic sulphantimoniate (Na^SbS^). 34. Sodium thioantimonate (NajSbS,). 35. Trisulphosodic sulphantimonate (Sb S"Nas3). 36. — XV. 1. 2. 3. 4. 5. 6. 7. 8. 10. 11. 12. 13. 14. 16. 16. 17. 18. 19. Fluat of potass and silica. Fluate of potash and silica. Fluosilicate of potash. Silico-fluate. Fluosilicate of potash. Silicofluoride of potassium (po + 2Si + 3f). Silicofluoride of potassium (po + 2Si + 3f). Double fluoride of silicon and potas- sium (2SiF3,3KF). Fluor-siliciumkalium (KF,SiFj). Fluorsiliciumkalium. Kieselfluor- kalium (SKF^/iSiFs). Fluorkiesel Kalium. Kalium-Kieselfluorid (3KF,2SiP3). Fluosilicate of potassium, silico- fluoride of potassium (SiF^ + KF). Double fluoride of silicon and potassium (2SiF3,3KF). Hydrofluosilicate de j^otasse (3KF1, 2SiFl3). Double fluoride of silicium and potassium (SKF.SiF,). Kieselfluorkalium. Fluorkieselkalium (3KaFl,2SiFl3, oder KaFl.SiFlJ. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. .35. 36. Silicofluoride of potassium (KF, SiF.). Hydrofluosilicate de potasse (3KF1, 2SiFl3). Silicofluoride of potassium. Potassic silicofluoride (2KF,SiFj). Fluorure double de sihcium et de potassium. Kieselfluorkalium. Double fluoride of silicium and potassium (2KF,SiFJ. Potassic fluosilicate (K.jSiFg). Fluosilicate de potassium. Silicofluoride of potassium (2KF, SiF,). Metallsilicofluoriire. Kieselfluormetalle (SiF^.MFj). Double fluoride of silicium and potassium (2KF,SiF,). Potassic silicofluoride. Silicofluoride. potassium fluosili- cate (K^SiFg). Potassic silicofluoride (SiFjK2 = Si F„2KF). Potassium fluosilicate. XVI. 1. 2. 3, 4. 5. 6. 7. 8. 10. 11. 12. 13. 14. 15. 16. 17. Muriat of platinum and potass. Muriate of platinum and potash. Bichloroplatinate of potassium. Platino-bichloride of potassium (pi + 2c) + (po + c). Platino-bichloride of potassium (pl+2c) + (po-i-c). Chloride of platinum and jjotassium (KCl + PtClj). Zweifach Chlorplatinkalium (KC1 + PtCU). Kaliumplatinchlorid (KClj + PtClJ. Kaliumplatinchlorid. Kalium-platinchlorid (KOi + PtGi^)- Platinchlorid-chlorkalium. Double salt of bichloride of platinum with chloride of potassium (KCl + PtCL). Chloroplatinate of potassium (KCl, PtClj). Chlorure double de platine et de potassium (PtCl, + KCl). 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. Bichloride of platinum and chloride of potassium (PtClj.KCl). Kalium-platinchlorid. Kalium-chlo- roplatinat (KaCl.PtClj). Double chloride of platinum and potassium (KCl.PtCl,,). Chlorure double de platine et de potassium (PtCL -i- KCl). Chloroplatinate of potassium, 1866. potassium platinochloride (KjPt CIJ. Supp. I. 1872. Chlorure double de platine et de potassium. Kaliumplatinchlorid. Potassium platinochloride (2KC1, PtCl,). Chloroplatinate de potassium. Platinochloride of potassium (2KC1, PtCl,). Kaliumplatinchlorid. Kaliumplatinchlorid (2KCl,PtCl4). Potassium platinochloride or chloro- platinate (2KCl,PtCl<). ON CHEMICAL NOMENCLATURE. 275 33. Potassic platinic chloride. 34. Potassium platinichloride or chloro- platinate (KjPtClJ. 35. Potassic platinic chloride (PtCl., 2KC1). 36. Potassium chlorplatinate. XVII. 1. — 2. — 3. — 4. — 5. — 6. Cyanuret of platinum and potassium. 7. — 8. Cyanuret of platinum and potas- sium. 9. Platino-cyanide of potassium (K, PtCy^ + SHO). Einfach-cyanplatinkalium (KCy, PtCy). 10. 11. 12. 13. U. 15. 16. 17. 18. 1. 2. 3. 4. 6. «. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16, 17. Kalium Platincyaniir (K6y, + Pt6y + 3H). Kalium Platincyaniir (K6y + Pt€y + 3H0). Platinocyanide of potassium (PtCy + KCy or K,Cpty). Platinocyanides (MCy.PtCy). Cyanure double de platine et de po- tassium (KCy + PtCy + 3H0). 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. Kaliumplatincyaniir -(-3H0). (KaCy.PtCy XVIII. 18. 19. 20. 21. 22. 23. Acetate and arsenite of copper, CuO, (C^H303) + 3 (CuO.AsOj). Essigarsenigsaures Kupferoxyd, 3(CuO,As03) + C^HjCuO^. Essigsaures Kupferoxid und Arsenig- saures Kupferoxid, A,CuO + 3(As03, CuO). Arsenichtsaures und essigsaiires Kupferoxyd, (CuA + 3Cu-As). Arsenigessigsaures Kupferoxyd. Compound of acetate of copper, and arsenite of copper, CuO.A -f-3(H0.2CuO-hAs03). Acetate and arsenite of copper, CuO, (C^H303) + 3 (CuO.As,03). Une combinaison, CuO. C.H3O3 + 3(2CuO.AsO,). 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. Cyanure double de platine et de potassium (KCy -1- PtCy -t- 3H0). Platinocyanide of potassium (K..Pt Cy^ = 2KCy,PtCy,), 1866. Potassic platinous cyanide (KjPtCyJ. Supp. I. 1872. Plantinocyanure de potassium, (Pt CyOK- + 3H-0. Kaliumplatincyaniir. Kaliumplatincyaniir (2KCy,PtCy2). Potas.sium platinocyanide, K2Pt(CN). + I2H2O. Potassium platinous cyanide. Eine Verbindung, CuO.AcOj + 3(2CuO,A.s03). CuO,CjH303 + 3 (CuO.AsOj). CuO,C,H303 + 3 (2Cu0,As03). Aceto-arsenite of copper (CoHjOj)^ Cu", 3 (As02)2 Cu" or C^H.O*. Cu"0 + 3 (AsACu"0). Cupric acetoarsenite, Cu(As02) (C2H3O2). Un acetoarsenite. Arsenigessigsaures Kupfer, Cu.,(OAsO) 3 (OC2H3O). Cupric arsenite and acetate, SCuAsjOj. Cu (CjHjO^),. Copper acetoarsenite, SCuASjO. + Cu(C2H302)2. Double compound. T 2 276 REPOET — 1885. RepoH of the Committee, consisting of Professors Odllxg, Hunt- ington, and Hartley, ai^'pointed to investigate by means of Photography the Ultra-Violet Spark Spectra emitted by Metallic Elements, and their combinations under varying conditions, Braxon up by Professor W. N. Hartley, F.R.S. {Secretary.) The last Report of this Committee was presented at the Sotithport meet- ino- of the British Association ; since then an investigation in detail has bera prosecuted of the changes observable in photographs of the spectra of the metals when a series of solutions of definite strengths is examined. It had previously been shown that solutions containing the same element in different proportions emit variations of the same spectrum, the lines differing in number, length, and intensity ; and the converse— namely, that under the same spark conditions similar solutions of the same strength always emit the same spectrum. Furthermore, I have shown the invariable character of the cadmium, tin, lead, and magnesium lines by observations made on about five thousand photographs, including not fewer than two hundred examples of other metals. The reason of this arises from the fact that unless the spark be almost at the highest tempera- ture attainable, its emissive power is insufficient to affect the photographic plate in the usual period of exposure ; it follows from this that when a condenser of constant capacity is in circuit, variable conditions such as may be introduced by the electrodes being near together or far apart, or by the use of a large or small coil, do not affect the result. Sparks are shortened and the character of the spectra is greatly altered by the use of a coil with a stout secondary wire, an instrument introduced and employed by M. Eugene Demarfay. The use of an instrument of this kind is not well adapted to the photographic method of working, because the nature of the sparks is such that the graphite electrodes are rapidly burnt away and the sparks are very short. For the examination of solutions chlorides are generally employed, but sulphates and nitrates are also used. The electrodes are nearly always of graphite (' Phil. Trans.' p. 52, Part I. 1884) ; sometimes gold,, copper, or platinum electrodes are required for special purposes, wires of the metal being twisted into wicks. The solutions examined generally contained 1 per cent., -^i\ xrcrtn, and ToW*^ °f metal. It is seldom that more than three or four lines are visible in solutions of the latter dilution, and the rapidly diminishing number of lines in solutions weaker than -^^ih per cent, is very striking. In the following tables the spectra corresponding to various solutions are given, and attention is particularly directed to the copper, silver, and tin. spectra as illustrating this point. In many spectra it is impossible to predict the line or lines which will be found to be the most persistent. It ia also noticeable that the alteration of lines consequent on the dilution of solutions is variable in character with different lines in the same spectrum. Generally speaking, long lines shorten until they disappear, sometimes they become attenuated before they shorten, and in other cases they attenuate until they fade away altogether. The calcium lines H and K attenuate considerably before they shorten,, while the lines of copper with wave-lengths 3273-2 and 3246-9, and of silver, 33828 and 3280-1, attenuate and fade almost away before shortening. ON THE DLTBA-VIOLET SPAEK SPECTRA. 277 Several examples could be quoted of the analysis of minerals made by the spectroscope, the metallic constituents being estimated quantita- tively with exactitude and great faciUty. In some cases the results obtained by the spectroscope inspire greater confidence than those made by ordinary methods. The descriptive tables which follow are intended to be used with maps drawn to the scale of wave-lengths, and to a scale of actual mea- surements taken from photographs, so that the lines may be readily identified. The scale numbers given in the tables in hundredths of an inch refer to photographs such as those published in the ' Journal of the Chemical Society ' (' Trans.' vol. xli. p. 90, 1882), from which actual measurements may be taken -with an ivory scale. The limit of sensitiveness of the spectrum reaction is perhaps the greatest in the case of magnesium ; one part of the metal in 10,000 millions of solution is easily detected by the appearance of the lines with wave-lengths 2801 "6 and 2794"1 attenuated and shortened. By increasing the strength of the spark the sensitiveness may be magnified 10,000 fold. It was shown in the Report presented in 1883 how spectrum observa- tions may be applied to determining the atomic weight of an element. Taking into account the spectrum of berylUam, this metal could find no place among the triad elements, but naturally took a position at the head of the dyad group. According to the periodic law its atomic weight would thus have the value 9. This view was opposed at the time, but it is satisfactory to learn that it has since been completely confirmed by the experimental work of Messrs. Nilson and Pettersoa and Dr. Humpidge. The Zinc Spectrum. Scale numbers Wave-lengths 1 per cent. 0-1 per cent. 0-01 per cent. Hundredths of an inch 108-49 113-75 116-30 145-69 194-98 252-31 267-95 3344-4 3301-7 3281-7 3075-6 2800-1 2557-3 2501-5 3344-4 3301-7 3281-7 3075-6 2800-1 ? 2557-3 2501-5 3344-4 3301-7 3281-7 The Thallium Spectrum. Scale numbers Wave-lengths 1 per cent. 0-1 per cent. 0-01 per cent. Hundredths of an inch 64-55 88-7 143-0 172-21 201-87 259-86 335-27 3775-6 3518-6 3091-0 2917-7 2767-1 2530-0 2299-3 3775-6 .3518-6 3091-0 2767-1 2530-0 2299-3 3775-6 2767-1 278 EEPOET 1885. The Cadmium Spectrum. Wave-lengths Scale numbers 1 per cent. 0-1 per cent. 0-01 per cent. 0-001 percent. Hundredths of an inch 79-37 / 3612-0 \ 3609-6 36120 3612-0 79-68 3609-6 3609-6 94-30 / 3466-7 \ 3465-2 3466-7 3466-7 94-50 3465-2 3465-2 101-45 3402-8 3402-8 1190 3260-2 205-87 2747-7 2747-7 248-24 2572-3 2572-3 326-8 f 2321 -6 2313-5 329-85 2313-5 2313-5 339-25 ■ 2288-8 2265-8 2288-8 2288-8 348-15 2265-8 2265-8 2265-8 377-48 2196-4 400-2 2146-8 The Aluminium Spectrum. Wave-lengths Scale numbers 1 per cent. 0-1 per cent. 0-01 per cent. 0-001 per cent. Hundredtlis of an inch f 49-85 1.51-16 / 3960-9 .3960-9 3960-9 3960-9 ? 1.3943-4 3943-4 3943-4 3943-4 ? The air-lines conti; ^uous to the abo\ -e are very strong, hence it is a little doubtful whether they are pres ent in the spectr um of a solution so dilute as 001 per cent. / 70-02 171-05 f 371 3-4 13701-5 r 79-17 180-5 f3612-4 13601-1 3612-4 3612-4 36011 3601-1 82-07 3584-4 r 142 86 1.144-5 / 3091-8 .3091-8 3091-8 .3091-8 1.3081-2 3081-2 3081-2 3081-2 148-5 3056 6 191-76 2815-3 2815-3 2815-3 2815-3 226-3 2659-3 2659-3 228-26 2651-2 2651-2 249-66 2566-9 2566-9 308-55 2373-3 309-0 2372-0 309-6 2370-2 309-94 2367-2 310-62 2364-5 The line with -wave-lengtli 3584"'4 is both much longer and stronger than either 3612'6 or 3601-2, yet it is not so persistent. From appear- ing as a strong line it disappears rather suddenly. The line -v^ith -wave-length 28153 is the strongest in this epectrum. ON THE ULTRA-VIOLET SPARK SPECTRA. 279 Tabular Description of the Spectra characteristic of Solutions containing Magnesium. Wave-lengths of the lines visible Scale numbers Parts of magnesium per 100 of solution 10 1 0-1 0-03 0-02 0-01 0-003 0-002 0-001 per cent. per per per per per per per per cent. cent. cent. cent. 1 cent. cent. cent. cent. Hundredths of an inch 17-46 4480 4480 4480 69-30 r 3837-9 3837-9 3837-9^3837-9 3837-9 59-83 ■{ 38321 38321 3832-1*3832-1 3832-1 60-07 3829-2 3829-2 3829-2 142-3 r 3096-2 ■I 3091-9 L 3089-9 3096-2 3096-2 142-85 3091-9 3091-9 143-18 3089-9 3089-9 168-7 / 2935-9 \ 2928-2 2935-9 2935-9 2935-9 2935-9 2935-9 2935-9 2935-9 2935-9 170-18 2928-2 2928-2 2928-2 2928-2 2928-2 2928-2 2928-2 2928-2 184-63 2851-2 2851-2 2851-2 2851-2 2851-2 2851-2 2851-2 2851-2 2851-2 194-55 r2801-6 2801-6 2801-6 2801-6 2801-6 2801-6 2801-6 2801-6 2801-6 195-39 I 2796-9 2796-9 2796-9 2796-9 2796-9 2796-9 2796-9 2796-9 2796-9 195-95 ' 2794-1 2794-1 2794-1 2794-1 2794-1 2794 1 2794-1 2794-1 2794-1 196-92 [2789-6 2789-6 2789-6 2789-6 2789-6 2789-6 2789-6 2789-6 2789-6 198-64 (-2781-8 2781-8 2781-8 2781-8 1 198-96 2780-2 1 199-3 .' 2778-7 2778-7 2778-7 2778-7 2778-7 2778-7 199-61 2776-9 199-97 I2775-5 2775-5 2775-5 A line ma}' be shortened or -weakened, but its -wave-length in this table denotes that although it may be changed it is still visible. The numbers bracketed are the wave-lengths of characteristic groups of lines. The Indium Spectrum. Scale numbers Wave-lengths 1 per cent. 0-1 per cent. 001 per cent. Hundredths of an inch 15-88 39-91 119-31 119-68 151-35 168-00 177-34 214-56 251-76 332-2 4510-2 4101-3 3257-8 3255-5 3038-7 2940-8 2889-7 2709-3 2559-5 2307 4510-2 4101-3 3255-5 3038-7 2940-8 2889-7* 2709-3 2307 3255-5 3038-7 This is barely visible. 280 EEPORT — 1885. The Copioer Spectrum. Wave-lengths Scale numbers 1 per cent. 0-1 per cent. 0-01 per cent. 0-001 per cent. Hundredths of an inch 11310 3306-8 3306-8 115-10 3289-9 r 117-25* / 3273-2 13246-9 3273-2 3273-2 1 120-7 3246-9 3246-9 3246-9 164-53 2959-5 190-13 2823-2 201-36 2769-1 2769-1 211-8 2721-2 212-65 27] 8-4 2718-4 213-7 2713-0 2713-0 2161 - 2702-7 216-58 2700-5 219-37 2688-8 2688-8 224-7 2666-7 236-45t 2617-8 241-1 2599-7 241-58 2598-3 255-94 2544-6 2544-6 260-25 2528-8 2528-8 261-00 2526-2 266-77 2506-2 2506-2 270-91 2491-4 271-65 2489-1 272-72 2485-6 276-45 2473-2 298-31 2403-3 299-4 2400-1 r309-17 \ 309-57 /2371-6 12370-1 2371-6 2370-1 336-8 2295-0 343-67 2277-0 r356-27t r2248-2 2247-7 2248-2 j 355-5 2247-7 ] 357-1 2244-0 2243-5 2244-0 L357-32 2243-5 * This pair of lines differs from all others in the spectrum by not being shortened on dilution, but becoming attenuated till at last they disappear. They remain long lines till the last. f This is a very fine and very long line. X This group is distinctly seen to be composed of four lines in the photographs of the 1 per cent, solution, and some lines, to the number of four or five, more refrangible than these are visible. ON THE ULTEA-VIOLET SPARK SPECTRA. 281 The Silver Spectrum. Wave-lengths Scale numbers 1 per cent. 0-1 per cent. 0-01 per cent. 0-001 per cent. Hundredths of an inch 103-94 3382-3 3382-3 3382-3 116-45 3280-1 3280-1 3280-1 168-5 2937-6 169-3 2933-5 2933-6 170-17 2928-2 2928-2 175-02 2901-6 176-07 2895-6 180-44 2872-7 2872-7 191-82 2814-5 195-03 2798-8 201-81 2766-4 2766-4 204-2 2755-5 214-22 2711-3 2711-3 226-27 2659-6 2659-6 227-08 2656-2 246-3 2579-9 268-81 2506-0 25060 274-52 2479-9 275-41 2476-8 276-41 2473-3 2473-3 279-92 2462-2 280-52 2459-8 282-6 2453-0 284-38 2447-4 2447-4 287-46 2437-3 2437-3 2437-3 290-0 2429-8 2429-8 293-08 2419-9 2419-9 295-35 2413-3 2413-3 2413-3 2413-3 295-94 2411-3 2411-3 297-94 2406-4 298-85 2404-5 301-10 2395-7 302-74 2390-8 304-07 2386-7 305-25 2383-6 307-94 2376-5 311-70 2364-3 312-34 2362-3 313-47 2359-2 2359-2 313-88 2358 2358-0 323-35 2331-7 2331-7 2331-7 325-73 2325-3 2325-3 2325-3 327-37 2320-5 2320-5 2320-5 328-59 2317-4 2317-4 2317-4 342-55 2280-7 2280-7 354-95 2249-9 2249-9 354-90 2247-6 2247-6 2247-6 362-86 2230-6 282 REPORT 1885. The Mercury Spectrum. Scale numbers Wave-lengths 1 per cent. 0-1 per cent. 0-01 per cent. Hundredths of an inch r 74-6 < 75-37 L 77-37 r 137-08 i 137-95 163-37 185-45 258-75 364-51 f 3662-9 { 3654-4 L3632-9 /3130-4 13124-5 2966-4 2846-8 2533-8 2225-7 3632-9 3130-4 2966-4 2533-8 2533-8 The Tin Spectrum. Wave-lengths Scale numbers 1 per cent. 0-1 per cent. 0-01 per cent. Hundredths of an inch 62-40 3800-3 3800-3 ri07-51 '3351-8 J 3329-9 3351-8 1 110-25 3329-9 1 11603 ' 3282-9 3261-6 3282-9 tll8-83 3261-6 130-7 3174-3 3174-3 /152-18 1156-29 / 3033-0 13007-9 3033-0 3007-9 173-05 2912-0 176-18 2895-0 177-8 2886-9 ri82-47 r28620 2862-0 2862-0 \ 184-99 { 2849-2 Ll87-01 L2833-9 2833-9 192-3 2812-5 2812-5 198-28 2784-0 199-34 2778-8 2778-8 215-35 2705-8 2705-8 2705-8 ' 224-95 '2664-2 225-98 2660-6 226-56 2657-9 2657-9 t 229-67 * 2645-4 230-23 2643-2 2643-2 233-17 2631-4 2631-4 '242-65 "2593-6 243-10 2591-7 248-70 2570-5 2570-5 255-45 2545-6 2545-6 r269-8 1273-4 f 2495-0 12482-9 2482-9 / 289-95 1292-37 / 2429-3 12421-8 2429-3 2429-3 2421-8 310-11 2368-3 314-85 2355-0 23550 321-94 2335-3 328-34 2317-9 355-83 2247-0 ON THE IJLTEA-VIOLET SPARK SPKCTEA. 283 The Lead Spectrum. Wave-lengths Scale numbers 1 per cent. 0-1 per cent.